Lagrange.cc 179 KB
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#include "Mesh.h"
#include "Element.h"
#include "Lagrange.h"
#include "DOFAdmin.h"
#include "RCNeighbourList.h"
#include "DOFVector.h"
#include "Traverse.h"
#include "Line.h"
#include "Triangle.h"
#include "Tetrahedron.h"
#include "Parametric.h"

#include <stdio.h>
#include <algorithm>
#include <list>

namespace AMDiS {

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  std::vector<DimVec<double>* > Lagrange::baryDimDegree[MAX_DIM + 1][MAX_DEGREE + 1];
  DimVec<int>* Lagrange::ndofDimDegree[MAX_DIM + 1][MAX_DEGREE + 1];
  int Lagrange::nBasFctsDimDegree[MAX_DIM + 1][MAX_DEGREE + 1];
  std::vector<BasFctType*> Lagrange::phiDimDegree[MAX_DIM + 1][MAX_DEGREE + 1];
  std::vector<GrdBasFctType*> Lagrange::grdPhiDimDegree[MAX_DIM + 1][MAX_DEGREE + 1];
  std::vector<D2BasFctType*> Lagrange::D2PhiDimDegree[MAX_DIM + 1][MAX_DEGREE + 1];
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  std::list<Lagrange*> Lagrange::allBasFcts;
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  Lagrange::Lagrange(int dim, int degree)
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    : BasisFunction(std::string("Lagrange"), dim, degree)
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  {
    // set name
    char dummy[3];
    sprintf(dummy, "%d", dim);
    name.append(dummy);
    name.append(" ");
    sprintf(dummy, "%d", degree);  
    name.append(dummy);

    // set nDOF
    setNDOF();

    // set barycentric coordinates
    setBary();

    // set function pointer
    setFunctionPointer();

  }

  Lagrange::~Lagrange()
  {
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    for (int i = 0; i < static_cast<int>(bary->size()); i++) {
      if ((*bary)[i]) {
	DELETE (*bary)[i];
	(*bary)[i] = NULL;
      }
    }
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  }

  Lagrange* Lagrange::getLagrange(int dim, int degree)
  {
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    std::list<Lagrange*>::iterator it;
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    for (it = allBasFcts.begin(); it != allBasFcts.end(); it++) {
      if (((*it)->dim == dim) && ((*it)->degree == degree)) {
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	return (*it);
      } 
    }

    Lagrange* newLagrange = NEW Lagrange(dim, degree);
    allBasFcts.push_back(newLagrange);
    return newLagrange;
  }

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  void Lagrange::clear()
  {    
    std::list<Lagrange*>::iterator it;
    for (it = allBasFcts.begin(); it != allBasFcts.end(); it++) {
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      if (*it) {
	DELETE *it;
	*it = NULL;
      }     
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    }
  }

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  void Lagrange::setFunctionPointer()
  {
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    if (static_cast<int>(phiDimDegree[dim][degree].size()) == 0) {
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      // for all positions
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      for (int i = 0; i < dim+1; i++) {
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	// no vertex dofs for degree 0 ?
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	if (degree == 0 && i != dim) 
	  continue;
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	// for all vertices/edges/...
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	for (int j = 0; j < Global::getGeo(INDEX_OF_DIM(i, dim),dim); j++) {
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	  // for all dofs at this position
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	  for (int k = 0; k < (*nDOF)[INDEX_OF_DIM(i, dim)]; k++) {
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	    // basis function
	    phiDimDegree[dim][degree].push_back(NEW Phi(this, 
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							INDEX_OF_DIM(i ,dim),j, k));
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	    // gradients
	    grdPhiDimDegree[dim][degree].push_back(NEW GrdPhi(this, 
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							      INDEX_OF_DIM(i, dim),
							      j, k));
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	    // D2-Matrices
	    D2PhiDimDegree[dim][degree].push_back(NEW D2Phi(this, 
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							    INDEX_OF_DIM(i, dim),
							    j, k));
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	  }
	}
      }
    }
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    phi = &phiDimDegree[dim][degree];
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    grdPhi = &grdPhiDimDegree[dim][degree];
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    d2Phi = &D2PhiDimDegree[dim][degree];
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    switch(degree) {
    case 0:
      refineInter_fct = refineInter0;
      coarseRestr_fct = coarseRestr0;
      coarseInter_fct = coarseInter0;  // not yet implemented
      break;
    case 1:
      refineInter_fct = refineInter1;
      coarseRestr_fct = coarseRestr1;
      coarseInter_fct = NULL;  // not yet implemented
      break;
    case 2:
      switch(dim) {
      case 1:
	refineInter_fct = refineInter2_1d;
	coarseRestr_fct = NULL; // not yet implemented
	coarseInter_fct = coarseInter2_1d;
	break;
      case 2: 
	refineInter_fct = refineInter2_2d;
	coarseRestr_fct = coarseRestr2_2d;
	coarseInter_fct = coarseInter2_2d;
	break;
      case 3:
	refineInter_fct = refineInter2_3d;
	coarseRestr_fct = coarseRestr2_3d;
	coarseInter_fct = coarseInter2_3d;
	break;
      default: ERROR_EXIT("invalid dim\n");
      }
      break;
    case 3:
      switch(dim) {
      case 1:
	refineInter_fct = refineInter3_1d;
	coarseRestr_fct = coarseRestr3_1d;
	coarseInter_fct = coarseInter3_1d;
	break;
      case 2: 
	refineInter_fct = refineInter3_2d;
	coarseRestr_fct = coarseRestr3_2d;
	coarseInter_fct = coarseInter3_2d;
	break;
      case 3:
	refineInter_fct = refineInter3_3d;
	coarseRestr_fct = coarseRestr3_3d;
	coarseInter_fct = coarseInter3_3d;
	break;
      default: ERROR_EXIT("invalid dim\n");
      }
      break;
    case 4:
      switch(dim) {
      case 1: 
	refineInter_fct = refineInter4_1d;
	coarseRestr_fct = coarseRestr4_1d;
	coarseInter_fct = coarseInter4_1d;
	break;
      case 2:
	refineInter_fct = refineInter4_2d;
	coarseRestr_fct = coarseRestr4_2d;
	coarseInter_fct = coarseInter4_2d;
	break;
      case 3:
	refineInter_fct = refineInter4_3d;
	coarseRestr_fct = coarseRestr4_3d;
	coarseInter_fct = coarseInter4_3d;
	break;
      default: ERROR_EXIT("invalid dim\n");
      }
      break;
    default:
      ERROR_EXIT("invalid degree\n");
    }
  }

  void Lagrange::setNDOF()
  {
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    if (static_cast<int>(baryDimDegree[dim][degree].size()) == 0) {
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      ndofDimDegree[dim][degree] = NEW DimVec<int>(dim, DEFAULT_VALUE, 0);

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      if (degree != 0) {
	(*ndofDimDegree[dim][degree])[VERTEX] = 1;
      } else {
	(*ndofDimDegree[dim][degree])[VERTEX] = 0;
      }
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      for (int i = 1; i < dim + 1; i++) {
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	nBasFcts = getNumberOfDOFs(i, degree);
	(*ndofDimDegree[dim][degree])[INDEX_OF_DIM(i, dim)] = nBasFcts;
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	for (int j = 0; j < i; j++) {
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	  (*ndofDimDegree[dim][degree])[INDEX_OF_DIM(i, dim)] -= 
	    Global::getGeo(INDEX_OF_DIM(j, dim), i) * 
	    (*ndofDimDegree[dim][degree])[INDEX_OF_DIM(j, dim)];
	}
      }
      nBasFctsDimDegree[dim][degree] = nBasFcts;
    }
    nBasFcts = nBasFctsDimDegree[dim][degree];
    nDOF = ndofDimDegree[dim][degree];
  } 

  DimVec<double> *Lagrange::getCoords(int i) const
  {
    return (*bary)[i];
  }

  void Lagrange::setVertices(int dim, int degree, 
			     GeoIndex position, int positionIndex, int nodeIndex, 
			     int** vertices)
  {
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    TEST_EXIT_DBG((*vertices) == NULL)("vertices != NULL\n");
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    int dimOfPosition = DIM_OF_INDEX(position, dim);

    *vertices = GET_MEMORY(int, dimOfPosition + 1);

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    if ((degree == 4) && (dimOfPosition==1)) {
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      (*vertices)[(nodeIndex != 2) ? 0 : 1] = 
	Global::getReferenceElement(dim)->getVertexOfPosition(position,
							      positionIndex,
							      0);
      (*vertices)[(nodeIndex != 2) ? 1 : 0] = 
	Global::getReferenceElement(dim)->getVertexOfPosition(position,
							      positionIndex, 
							      1);
    } else if ((degree==4) && (dimOfPosition==2)) {
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      for (int i = 0; i < dimOfPosition + 1; i++) {
	(*vertices)[(i+dimOfPosition*nodeIndex) % (dimOfPosition + 1)] = 
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	  Global::getReferenceElement(dim)->getVertexOfPosition(position,
								positionIndex,
								i);
      }    
    } else {
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      for (int i = 0; i < dimOfPosition + 1; i++) {
	(*vertices)[(i+nodeIndex) % (dimOfPosition + 1)] = 
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	  Global::getReferenceElement(dim)->getVertexOfPosition(position,
								positionIndex,
								i);
      }
    }
  }

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  Lagrange::Phi::Phi(Lagrange* owner, 
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		     GeoIndex position, 
		     int positionIndex, 
		     int nodeIndex)
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    : vertices(NULL)
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  {
    FUNCNAME("Lagrange::Phi::Phi")
      // get relevant vertices
      Lagrange::setVertices(owner->getDim(), 
			    owner->getDegree(), 
			    position, 
			    positionIndex, 
			    nodeIndex, 
			    &vertices);
  
    // set function pointer
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    switch (owner->getDegree()) {
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    case 0:
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      switch (position) {
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      case CENTER:
	func = phi0c;
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 1:
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      switch (position) {
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      case VERTEX:
	func = phi1v;
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 2:
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      switch (position) {
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      case VERTEX:
	func = phi2v;
	break;
      case EDGE:
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	TEST_EXIT_DBG(owner->getDim() > 1)("no edge in 1d\n");
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	func = phi2e;
	break;
      case CENTER:
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	TEST_EXIT_DBG(owner->getDim() == 1)("no center dofs for dim != 1\n");
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	func = phi2e;
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 3:
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      switch (position) {
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      case VERTEX:
	func = phi3v;
	break;
      case EDGE:
	func = phi3e;
	break;
      case FACE:
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	TEST_EXIT_DBG(owner->getDim() >= 3)("no faces in dim < 3\n");
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	func = phi3f;
	break;
      case CENTER:
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	switch (owner->getDim()) {
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	case 1:
	  func = phi3e;
	  break;
	case 2:
	  func = phi3f;
	  break;
	default:
	  ERROR_EXIT("invalid dim\n");
	  break;
	}
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 4:
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      switch (position) {
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      case VERTEX:
	func = phi4v;
	break;
      case EDGE:
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	if (nodeIndex == 1)
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	  func = phi4e1;
	else 
	  func = phi4e0;
	break;
      case FACE:
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	TEST_EXIT_DBG(owner->getDim() >= 3)("no faces in dim < 3\n");
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	func = phi4f;      
	break;
      case CENTER:
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	switch (owner->getDim()) {
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	case 1:
	  if(nodeIndex == 1)
	    func = phi4e1;
	  else 
	    func = phi4e0;
	  break;
	case 2:
	  func = phi4f;
	  break;
	case 3:
	  func = phi4c;
	  break;
	default:
	  ERROR_EXIT("invalid dim\n");
	  break;
	}
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    default:
      ERROR_EXIT("invalid degree\n");
    }
  }

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  Lagrange::Phi::~Phi() { 
    DELETE [] vertices; 
  }
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  Lagrange::GrdPhi::GrdPhi(Lagrange* owner, 
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			   GeoIndex position, 
			   int positionIndex, 
			   int nodeIndex)
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    : vertices(NULL)
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  {
    // get relevant vertices
    Lagrange::setVertices(owner->getDim(), 
			  owner->getDegree(), 
			  position, 
			  positionIndex, 
			  nodeIndex, 
			  &vertices);

    // set function pointer
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    switch (owner->getDegree()) {
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    case 0:
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      switch (position) {
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      case CENTER:
	func = grdPhi0c;
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 1:
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      switch (position) {
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      case VERTEX:
	func = grdPhi1v;
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 2:
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      switch (position) {
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      case VERTEX:
	func = grdPhi2v;
	break;
      case EDGE:
	func = grdPhi2e;
	break;
      case CENTER:
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	TEST_EXIT_DBG(owner->getDim() == 1)("no center dofs for dim != 1\n");
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	func = grdPhi2e;
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 3:
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      switch (position) {
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      case VERTEX:
	func = grdPhi3v;
	break;
      case EDGE:
	func = grdPhi3e;
	break;
      case FACE:
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	TEST_EXIT_DBG(owner->getDim() >= 3)("no faces in dim < 3\n");
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	func = grdPhi3f;
	break;
      case CENTER:
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	switch (owner->getDim()) {
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	case 1:
	  func = grdPhi3e;
	  break;
	case 2:
	  func = grdPhi3f;
	  break;
	default:
	  ERROR_EXIT("invalid dim\n");
	  break;
	}
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 4:
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      switch (position) {
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      case VERTEX:
	func = grdPhi4v;
	break;
      case EDGE:
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	if (nodeIndex == 1)
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	  func = grdPhi4e1;
	else 
	  func = grdPhi4e0;
	break;
      case FACE:
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	TEST_EXIT_DBG(owner->getDim() >= 3)("no faces in dim < 3\n");
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	func = grdPhi4f;      
	break;
      case CENTER:
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	switch (owner->getDim()) {
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	case 1:
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	  if (nodeIndex == 1)
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	    func = grdPhi4e1;
	  else 
	    func = grdPhi4e0;
	  break;
	case 2:
	  func = grdPhi4f;
	  break;
	case 3:
	  func = grdPhi4c;
	  break;
	default:
	  ERROR_EXIT("invalid dim\n");
	  break;
	}
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    default:
      ERROR_EXIT("invalid degree\n");
    }
  }

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  Lagrange::GrdPhi::~GrdPhi() { 
    DELETE [] vertices; 
  }
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  Lagrange::D2Phi::D2Phi(Lagrange* owner, 
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			 GeoIndex position, 
			 int positionIndex, 
			 int nodeIndex)
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    : vertices(NULL)
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  {
    // get relevant vertices
    Lagrange::setVertices(owner->getDim(), 
			  owner->getDegree(), 
			  position, 
			  positionIndex, 
			  nodeIndex, 
			  &vertices);

    // set function pointer
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    switch (owner->getDegree()) {
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    case 0:
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      switch (position) {
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      case CENTER:
	func = D2Phi0c;
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 1:
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      switch (position) {
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      case VERTEX:
	func = D2Phi1v;
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 2:
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      switch (position) {
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      case VERTEX:
	func = D2Phi2v;
	break;
      case EDGE:
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	TEST_EXIT_DBG(owner->getDim() > 1)("no edge in 1d\n");
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	func = D2Phi2e;
	break;
      case CENTER:
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	TEST_EXIT_DBG(owner->getDim() == 1)("no center dofs for dim != 1\n");
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	func = D2Phi2e;
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 3:
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      switch (position) {
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      case VERTEX:
	func = D2Phi3v;
	break;
      case EDGE:
	func = D2Phi3e;
	break;
      case FACE:
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	TEST_EXIT_DBG(owner->getDim() >= 3)("no faces in dim < 3\n");
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	func = D2Phi3f;
	break;
      case CENTER:
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	switch (owner->getDim()) {
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	case 1:
	  func = D2Phi3e;
	  break;
	case 2:
	  func = D2Phi3f;
	  break;
	default:
	  ERROR_EXIT("invalid dim\n");
	  break;
	}
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    case 4:
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      switch (position) {
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      case VERTEX:
	func = D2Phi4v;
	break;
      case EDGE:
	if(nodeIndex == 1)
	  func = D2Phi4e1;
	else 
	  func = D2Phi4e0;
	break;
      case FACE:
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	TEST_EXIT_DBG(owner->getDim() >= 3)("no faces in dim < 3\n");
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	func = D2Phi4f;      
	break;
      case CENTER:
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	switch (owner->getDim()) {
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	case 1:
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	  if (nodeIndex == 1)
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	    func = D2Phi4e1;
	  else 
	    func = D2Phi4e0;
	  break;
	case 2:
	  func = D2Phi4f;
	  break;
	case 3:
	  func = D2Phi4c;
	  break;
	default:
	  ERROR_EXIT("invalid dim\n");
	  break;
	}
	break;
      default:
	ERROR_EXIT("invalid position\n");
      }
      break;
    default:
      ERROR_EXIT("invalid degree\n");
    }
  }

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  Lagrange::D2Phi::~D2Phi() { 
    DELETE [] vertices; 
  }
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  void Lagrange::createCoords(int* coordInd, 
			      int numCoords, 
			      int dimIndex, 
			      int rest, 
			      DimVec<double>* vec)
  {
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    if (vec == NULL) {
      vec = NEW DimVec<double>(dim, DEFAULT_VALUE, 0.0);
    }
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    if (dimIndex == numCoords - 1) {
      (*vec)[coordInd[dimIndex]] = double(rest) / degree;
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      DimVec<double>* newCoords = NEW DimVec<double>(*vec);
      bary->push_back(newCoords);
    } else {
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      for (int i = rest - 1; i >= 1; i--) {
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	(*vec)[coordInd[dimIndex]] = double(i) / degree;
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	createCoords(coordInd, numCoords, dimIndex + 1, rest - i, vec);
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      }
    }
  }

  void Lagrange::setBary()
  {
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    bary = &baryDimDegree[dim][degree];
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    if (static_cast<int>(bary->size()) == 0) {
      for (int i = 0; i <= dim; i++) { // for all positions
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	int partsAtPos = Global::getGeo(INDEX_OF_DIM(i, dim), dim);
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	for (int j = 0; j < partsAtPos; j++) { // for all vertices/edges/faces/...
	  int *coordInd = GET_MEMORY(int, i + 1); // indices of relevant coords
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	  for (int k = 0; k < i + 1; k++) { 
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	    coordInd[k] = Global::getReferenceElement(dim)->
	      getVertexOfPosition(INDEX_OF_DIM(i,dim), j, k);
	  }
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	  createCoords(coordInd, i + 1, 0, degree);
	  FREE_MEMORY(coordInd, int, i + 1);
	  if(static_cast<int>(bary->size()) == nBasFcts) return;
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	}
      }
    }
  }

  int Lagrange::getNumberOfDOFs(int dim, int degree)
  {
    int result = 0;
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    for (int i = 0; i <= degree; i++) {
      result += fac(dim - 1 + i) / (fac(i) * fac(dim - 1));
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    }
    return result;
  }


  const DegreeOfFreedom *Lagrange::getDOFIndices(const Element *el, 
						 const DOFAdmin& admin,
						 DegreeOfFreedom *idof) const
  {
    WARNING("depricated: use getLocalIndices() instead\n");
    return getLocalIndices(el, &admin, idof);
  }

  int* Lagrange::orderOfPositionIndices(const Element* el, 
					GeoIndex position, 
					int positionIndex) const
  {
    static int sortedVertex = 0;
    static int sortedEdgeDeg2 = 0;
    static int sortedEdgeDeg3[2][2] = {{0, 1}, {1, 0}};
    static int sortedEdgeDeg4[2][3] = {{0, 1, 2}, {2, 1, 0}};
    static int sortedFaceDeg3 = 0;
    static int sortedFaceDeg4[7][3] = {{0,0,0}, {0,2,1}, {1,0,2}, {0,1,2},
				       {2,1,0}, {1,2,0}, {2,0,1}};
    static int sortedCenterDeg4 = 0;

    int dimOfPosition = DIM_OF_INDEX(position, dim);

    // vertex
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    if (dimOfPosition == 0) {
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      return &sortedVertex;
    }

    // edge
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    if ((dimOfPosition == 1) && (degree == 2)) {
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      return &sortedEdgeDeg2;
    }
      
    int vertex[3];
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    int** dof = const_cast<int**>(el->getDOF());
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    int verticesOfPosition = dimOfPosition + 1;

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    for (int i = 0; i < verticesOfPosition; i++) {
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      vertex[i] = Global::getReferenceElement(dim)->
	getVertexOfPosition(position, positionIndex, i);
    }

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    if (dimOfPosition == 1) {
      if (degree == 3) {
	if (dof[vertex[0]][0] < dof[vertex[1]][0]) {
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	  return sortedEdgeDeg3[0];
	} else {
	  return sortedEdgeDeg3[1];
	}
      } else { // degree == 4
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	if (dof[vertex[0]][0] < dof[vertex[1]][0]) {
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	  return sortedEdgeDeg4[0];
	} else {
	  return sortedEdgeDeg4[1];
	}
      }
    }

    // face
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    if (dimOfPosition == 2) {
      if (degree == 3) {
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	return &sortedFaceDeg3;
      } else {  // degree == 4!
	int no = 0;
	const Element *refElem = Global::getReferenceElement(dim);

	if (dof[refElem->getVertexOfPosition(position, positionIndex, 0)][0] <
	    dof[refElem->getVertexOfPosition(position, positionIndex, 1)][0]) 
	  no++;

	if (dof[refElem->getVertexOfPosition(position, positionIndex, 1)][0] <
	    dof[refElem->getVertexOfPosition(position, positionIndex, 2)][0])
	  no += 2;

	if (dof[refElem->getVertexOfPosition(position, positionIndex, 2)][0] <
	    dof[refElem->getVertexOfPosition(position, positionIndex, 0)][0])
	  no += 4;

	return sortedFaceDeg4[no];
      }
    }

    // center
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    if ((dimOfPosition == 3) && (degree == 4)) {
      return &sortedCenterDeg4;
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    } 

    ERROR_EXIT("should not be reached\n");
    return NULL;
  }

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  void Lagrange::getBound(const ElInfo* el_info, BoundaryType* bound) const
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  {
    el_info->testFlag(Mesh::FILL_BOUND);

    // boundaries
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    int index = 0;
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    int offset = 0;
    BoundaryType boundaryType;
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    for (int i = dim - 1; i > 0; i--)
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      offset += Global::getGeo(INDEX_OF_DIM(i, dim), dim);
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    for (int i = 0; i < dim; i++) {
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      int jto = offset + Global::getGeo(INDEX_OF_DIM(i, dim), dim);
      for (int j = offset; j < jto; j++) {
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	boundaryType = el_info->getBoundary(j);
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	int kto = (*nDOF)[INDEX_OF_DIM(i, dim)];
	for (int k = 0; k < kto; k++) {
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	  bound[index++] = boundaryType;
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	}
      }
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      offset -= Global::getGeo(INDEX_OF_DIM(i + 1, dim), dim);
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    }

    // interior nodes in the center
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    for (int i = 0; i < (*nDOF)[CENTER]; i++) {
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      bound[index++] = INTERIOR;
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    }

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    TEST_EXIT_DBG(index == nBasFcts)("found not enough boundarys\n");
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  }


  const double* Lagrange::interpol(const ElInfo *el_info, 
				   int no, const int *b_no, 
				   AbstractFunction<double, WorldVector<double> > *f, 
				   double *vec)
  {
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    FUNCNAME("Lagrange::interpol()");

    static double *inter = NULL;
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    static int inter_size = 0;

    double *rvec =  NULL;

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    if (vec) {
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      rvec = vec;
    } else {
      if(inter) FREE_MEMORY(inter, double, nBasFcts);
      inter = GET_MEMORY(double, nBasFcts);
      inter_size = nBasFcts;
      rvec = inter;
    } 

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    WorldVector<double> x;
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    el_info->testFlag(Mesh::FILL_COORDS);
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    if (b_no) {
      if (no <= 0  ||  no > getNumber()) {
	ERROR("something is wrong, doing nothing\n");
	rvec[0] = 0.0;
	return(const_cast<const double *>( rvec));
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      }
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      for (int i = 0; i < no; i++) {
	if (b_no[i] < Global::getGeo(VERTEX, dim)) {
	  rvec[i] = (*f)(el_info->getCoord(b_no[i]));
	} else {
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	  el_info->coordToWorld(*(*bary)[b_no[i]], x);
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	  rvec[i] = (*f)(x);
	}
      }
    } else {
      int vertices = Global::getGeo(VERTEX, dim);
      for (int i = 0; i < vertices; i++)
	rvec[i] = (*f)(el_info->getCoord(i));
      for (int i = vertices; i < nBasFcts; i++) {
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	el_info->coordToWorld(*(*bary)[i], x);
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	rvec[i] = (*f)(x);
      }
    }  
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    return(const_cast<const double *>( rvec));
  }

  const WorldVector<double>* 
  Lagrange::interpol(const ElInfo *el_info, int no, 
		     const int *b_no,
		     AbstractFunction<WorldVector<double>, WorldVector<double> > *f, 
		     WorldVector<double> *vec)
  {
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    FUNCNAME("*Lagrange::interpol_d()");

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    static WorldVector<double> *inter;
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    WorldVector<double> *rvec = 
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      vec ? vec : (inter?inter:inter= NEW WorldVector<double>[getNumber()]);
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    WorldVector<double> x;
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    el_info->testFlag(Mesh::FILL_COORDS);
  
    int vertices = Global::getGeo(VERTEX, dim);

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    if (b_no) {
      if (no <= 0  ||  no > getNumber()) {
	ERROR("something is wrong, doing nothing\n");
	for (int i = 0; i < dow; i++)
	  rvec[0][i] = 0.0;
	return(const_cast<const WorldVector<double> *>( rvec));
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      }
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      for (int i = 0; i < no; i++) {
	if (b_no[i] < Global::getGeo(VERTEX, dim)) {
	  rvec[i] = (*f)(el_info->getCoord(b_no[i]));
	} else {
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	  el_info->coordToWorld(*(*bary)[b_no[i]], x);
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	  rvec[i] = (*f)(x);
	}
      }
    } else {
      for (int i = 0; i < vertices; i++)
	rvec[i] = (*f)(el_info->getCoord(i));
      for (int i = vertices; i < nBasFcts; i++) {
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	el_info->coordToWorld(*(*bary)[i], x);
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	rvec[i] = (*f)(x);
      }
    }  
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    return(const_cast<const WorldVector<double> *>( rvec));
  }


  const DegreeOfFreedom *Lagrange::getLocalIndices(const Element* el,
						   const DOFAdmin *admin,
						   DegreeOfFreedom *indices) const
  {
    static DegreeOfFreedom *localVec = NULL;
    static int localVecSize = 0;

    const DegreeOfFreedom **dof = el->getDOF();
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    int nrDOFs, n0, node0, num = 0;
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    GeoIndex posIndex;
    DegreeOfFreedom* result;
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    if (indices) {
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      result = indices;
    } else {
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      if (localVec) 
	FREE_MEMORY(localVec, DegreeOfFreedom, localVecSize);
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      localVec = GET_MEMORY(DegreeOfFreedom, nBasFcts);
      localVecSize = nBasFcts;
      result = localVec;
    }
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    for (int pos = 0, j = 0; pos <= dim; pos++) {
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      posIndex = INDEX_OF_DIM(pos, dim);
      nrDOFs = admin->getNumberOfDOFs(posIndex);

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      if (nrDOFs) {
	n0 = admin->getNumberOfPreDOFs(posIndex);
	node0 = admin->getMesh()->getNode(posIndex);
	num = Global::getGeo(posIndex, dim);

	for (int i = 0; i < num; node0++, i++) {
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	  const int *indi = orderOfPositionIndices(el, posIndex, i);
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	  for (int k = 0; k < nrDOFs; k++) {
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	    result[j++] = dof[node0][n0 + indi[k]];
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	  }
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	}
      }
    }
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    return result;
  }

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  void Lagrange::getLocalIndicesVec(const Element* el,
				    const DOFAdmin *admin,
				    Vector<DegreeOfFreedom> *indices) const
  {
    if (indices->getSize() < nBasFcts) {
      indices->resize(nBasFcts);
    }

    getLocalIndices(el, admin, &((*indices)[0]));
  }

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  void Lagrange::l2ScpFctBas(Quadrature *q,
			     AbstractFunction<WorldVector<double>, WorldVector<double> >* f,
			     DOFVector<WorldVector<double> >* fh)
  {
    ERROR_EXIT("not yet\n");
  }

  void Lagrange::l2ScpFctBas(Quadrature *q,
			     AbstractFunction<double, WorldVector<double> >* f,
			     DOFVector<double>* fh)
  {
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    FUNCNAME("Lagrange::l2ScpFctBas()");

    TraverseStack stack;
    double *wdetf_qp = NULL;
    double val, det;
    WorldVector<double> x;
    int iq, j;
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    const DegreeOfFreedom  *dof;
    const Parametric *parametric;

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    TEST_EXIT_DBG(fh)("no DOF_REAL_VEC fh\n");
    TEST_EXIT_DBG(fh->getFESpace())("no fe_space in DOF_REAL_VEC %s\n",
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				fh->getName().c_str());
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    TEST_EXIT_DBG(fh->getFESpace()->getBasisFcts() == this)("wrong basis fcts for fh\n");
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    Mesh* mesh = fh->getFESpace()->getMesh();
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    int n_phi = nBasFcts;
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    if (!q) {
      q = Quadrature::provideQuadrature(dim, 2 * degree - 2);
    }
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    const FastQuadrature *quad_fast = FastQuadrature::provideFastQuadrature(this, *q, INIT_PHI);
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    if ((parametric = mesh->getParametric())) {
      ERROR_EXIT("not yet implemented\n");
    } else {
      wdetf_qp = GET_MEMORY(double, q->getNumPoints());
    }
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    ElInfo *el_info = stack.traverseFirst(mesh, -1, Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS);
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    int numPoints = q->getNumPoints();
     
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    while (el_info) {
      dof = getLocalIndices(el_info->getElement(), (fh->getFESpace()->getAdmin()), NULL);      
      det = el_info->getDet();
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      for (iq = 0; iq < numPoints; iq++) {
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	el_info->coordToWorld(q->getLambda(iq), x);
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	wdetf_qp[iq] = q->getWeight(iq)*det*((*f)(x));
      }
      
      for (j = 0; j < n_phi; j++) {
	for (val = iq = 0; iq < numPoints; iq++)
	  val += quad_fast->getPhi(iq,j)*wdetf_qp[iq];
	(*fh)[dof[j]] += val;
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      }

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      el_info = stack.traverseNext(el_info);
    }

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    FREE_MEMORY(wdetf_qp, double, q->getNumPoints());

    return;
  }


  // ===== refineInter functions =====

  void  Lagrange::refineInter0(DOFIndexed<double> *drv, RCNeighbourList* list, int n, BasisFunction* basFct)
  {
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    FUNCNAME("Lagrange::refineInter0()");
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    if (n < 1) 
      return;

    int n0 = drv->getFESpace()->getAdmin()->getNumberOfPreDOFs(CENTER);
    Element *el = list->getElement(0);
    int node = drv->getFESpace()->getMesh()->getNode(CENTER);
    DegreeOfFreedom dof0 = el->getDOF(node, n0);           /* Parent center */
    DegreeOfFreedom dof_new = el->getChild(0)->getDOF(node, n0);  /*      newest vertex is center */
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    (*drv)[dof_new] = (*drv)[dof0];
    dof_new = el->getChild(1)->getDOF(node, n0);  /*      newest vertex is center */
    (*drv)[dof_new] = (*drv)[dof0];
  }

  void  Lagrange::refineInter1(DOFIndexed<double> *drv, RCNeighbourList* list, int n, BasisFunction* basFct)
  {
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    FUNCNAME("Lagrange::refineInter1_1d()");
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    if (n < 1) 
      return;
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    int dim = drv->getFESpace()->getMesh()->getDim();
    int n0 = drv->getFESpace()->getAdmin()->getNumberOfPreDOFs(VERTEX);
    Element *el = list->getElement(0);
    DegreeOfFreedom dof0 = el->getDOF(0, n0);           /* 1st endpoint of refinement edge */
    DegreeOfFreedom dof1 = el->getDOF(1, n0);           /* 2nd endpoint of refinement edge */
    DegreeOfFreedom dof_new = el->getChild(0)->getDOF(dim, n0);  /*      newest vertex is DIM */
    (*drv)[dof_new] = 0.5 * ((*drv)[dof0] + (*drv)[dof1]);
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  }

  void Lagrange::refineInter2_1d(DOFIndexed<double> *drv, RCNeighbourList* list, int n, BasisFunction* basFct)
  {
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    FUNCNAME("Lagrange::refineInter2_1d()");
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    if (n < 1) 
      return;
    
    Element *el = list->getElement(0);
    const DOFAdmin *admin = drv->getFESpace()->getAdmin();
    const DegreeOfFreedom *pdof = basFct->getLocalIndices(el, admin, NULL);
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    int node = drv->getFESpace()->getMesh()->getNode(VERTEX);        
    int n0 = admin->getNumberOfPreDOFs(VERTEX);
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    /****************************************************************************/
    /*  newest vertex of child[0] and child[1]                                  */
    /****************************************************************************/

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    DegreeOfFreedom cdof = el->getChild(0)->getDOF(node+1, n0);  /*      newest vertex is DIM */
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    (*drv)[cdof] = (*drv)[pdof[2]];

    node = drv->getFESpace()->getMesh()->getNode(CENTER);        
    n0 = admin->getNumberOfPreDOFs(CENTER);

    /****************************************************************************/
    /*  midpoint of edge on child[0] at the refinement edge                     */
    /****************************************************************************/
  
    cdof = el->getChild(0)->getDOF(node, n0); 
    (*drv)[cdof] = 
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      0.375 * (*drv)[pdof[0]] - 0.125 * (*drv)[pdof[1]] + 0.75 * (*drv)[pdof[2]];
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    /****************************************************************************/
    /*  midpoint of edge on child[1] at the refinement edge                     */
    /****************************************************************************/
  
    cdof = el->getChild(1)->getDOF(node, n0); 
    (*drv)[cdof] = 
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      -0.125 * (*drv)[pdof[0]] + 0.375 * (*drv)[pdof[1]] + 0.75 * (*drv)[pdof[2]];
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    return;
  }

  void Lagrange::refineInter2_2d(DOFIndexed<double> *drv, 
				 RCNeighbourList* list, 
				 int n, BasisFunction* basFct)
  {
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    FUNCNAME("Lagrange::refineInter2_2d()");
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    if (n < 1) 
      return;
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    const DOFAdmin *admin = drv->getFESpace()->getAdmin();
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    Element *el = list->getElement(0);
    const DegreeOfFreedom *pdof = basFct->getLocalIndices(el, admin, NULL);
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    int node = drv->getFESpace()->getMesh()->getNode(VERTEX);        
    int n0 = admin->getNumberOfPreDOFs(VERTEX);
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    /****************************************************************************/
    /*  newest vertex of child[0] and child[1]                                  */
    /****************************************************************************/

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    DegreeOfFreedom cdof = el->getChild(0)->getDOF(node+2, n0);  /*      newest vertex is DIM */
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    (*drv)[cdof] = (*drv)[pdof[5]];

    node = drv->getFESpace()->getMesh()->getNode(EDGE);        
    n0 = admin->getNumberOfPreDOFs(EDGE);

    /****************************************************************************/
    /*  midpoint of edge on child[0] at the refinement edge                     */
    /****************************************************************************/
  
    cdof = el->getChild(0)->getDOF(node, n0); 
    (*drv)[cdof] = 
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      0.375 * (*drv)[pdof[0]] - 0.125 * (*drv)[pdof[1]] + 0.75 * (*drv)[pdof[5]];
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    /****************************************************************************/
    /* node in the common edge of child[0] and child[1]                         */
    /****************************************************************************/

    cdof = el->getChild(0)->getDOF(node+1, n0); 
    (*drv)[cdof] =
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      -0.125 * ((*drv)[pdof[0]] + (*drv)[pdof[1]]) + 0.25 * (*drv)[pdof[5]]
      + 0.5 * ((*drv)[pdof[3]] + (*drv)[pdof[4]]);
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    /****************************************************************************/
    /*  midpoint of edge on child[1] at the refinement edge                     */
    /****************************************************************************/
  
    cdof = el->getChild(1)->getDOF(node+1, n0); 
    (*drv)[cdof] = 
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      -0.125 * (*drv)[pdof[0]] + 0.375 * (*drv)[pdof[1]]  + 0.75 * (*drv)[pdof[5]];

    if (n > 1) {
      /****************************************************************************/
      /*  adjust the value at the midpoint of the common edge of neigh's children */
      /****************************************************************************/
      el = list->getElement(1);
      pdof = basFct->getLocalIndices(el, admin, NULL);
      
      cdof = el->getChild(0)->getDOF(node+1, n0); 
      (*drv)[cdof] = 
	-0.125 * ((*drv)[pdof[0]] + (*drv)[pdof[1]]) + 0.25 * (*drv)[pdof[5]]
	+ 0.5 * ((*drv)[pdof[3]] + (*drv)[pdof[4]]);
    }
1180
1181
1182
1183
1184
1185
  }

  void Lagrange::refineInter2_3d(DOFIndexed<double> *drv, 
				 RCNeighbourList* list, 
				 int n, BasisFunction* basFct)
  {
1186
    FUNCNAME("Lagrange::refineInter2_3d()");
1187

1188
1189
    if (n < 1) 
      return;
1190

1191
1192
    Element *el = list->getElement(0);
    const DOFAdmin *admin = drv->getFESpace()->getAdmin();
1193

1194
    DegreeOfFreedom pdof[10];
1195
1196
    basFct->getLocalIndices(el, admin, pdof);

1197
1198
    int node0 = drv->getFESpace()->getMesh()->getNode(EDGE);
    int n0 = admin->getNumberOfPreDOFs(EDGE);
1199
1200
1201
1202
1203

    /****************************************************************************/
    /*  values on child[0]                                                      */
    /****************************************************************************/

1204
    const DegreeOfFreedom *cdof = basFct->getLocalIndices(el->getChild(0), admin, NULL);
1205
1206
1207

    (*drv)[cdof[3]] = ((*drv)[pdof[4]]);
    (*drv)[cdof[6]] = 
1208
1209
      (0.375 * (*drv)[pdof[0]] - 0.125 * (*drv)[pdof[1]] 
       + 0.75 * (*drv)[pdof[4]]);
1210
    (*drv)[cdof[8]] = 
1211
1212
      (0.125 * (-(*drv)[pdof[0]] - (*drv)[pdof[1]]) + 0.25 * (*drv)[pdof[4]]
       + 0.5 * ((*drv)[pdof[5]] + (*drv)[pdof[7]]));
1213
    (*drv)[cdof[9]] = 
1214
1215
      (0.125 * (-(*drv)[pdof[0]] - (*drv)[pdof[1]]) + 0.25 * (*drv)[pdof[4]]
       + 0.5 * ((*drv)[pdof[6]] + (*drv)[pdof[8]]));
1216
1217
1218
1219
1220

    /****************************************************************************/
    /*  values on child[1]                                                      */
    /****************************************************************************/
  
1221
    DegreeOfFreedom cdofi = el->getChild(1)->getDOF(node0 + 2, n0);
1222
    (*drv)[cdofi] = 
1223
1224
      (-0.125 * (*drv)[pdof[0]] + 0.375 * (*drv)[pdof[1]] 
       + 0.75 * (*drv)[pdof[4]]);
1225
1226
1227
1228
1229

    /****************************************************************************/
    /*   adjust neighbour values                                                */
    /****************************************************************************/
  
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
    for (int i = 1; i < n; i++) {
      el = list->getElement(i);
      basFct->getLocalIndices(el, admin, pdof);
      
      int lr_set = 0;
      if (list->getNeighbourElement(i, 0) && list->getNeighbourNr(i, 0) < i)
	lr_set = 1;
      
      if (list->getNeighbourElement(i, 1) && list->getNeighbourNr(i, 1) < i)
	lr_set += 2;
      
      TEST_EXIT(lr_set)("no values set on both neighbours\n");
      
      /****************************************************************************/
      /*  values on child[0]                                                      */
      /****************************************************************************/
      
      switch (lr_set) {
      case 1:
	cdofi = el->getChild(0)->getDOF(node0+4, n0);      
	(*drv)[cdofi] = 
	  (0.125 * (-(*drv)[pdof[0]] - (*drv)[pdof[1]]) + 0.25 * (*drv)[pdof[4]]
	   + 0.5 * ((*drv)[pdof[5]] + (*drv)[pdof[7]]));
	break;
      case 2:
	cdofi = el->getChild(0)->getDOF(node0+5, n0);      
	(*drv)[cdofi] = 
	  (0.125 * (-(*drv)[pdof[0]] - (*drv)[pdof[1]]) + 0.25 * (*drv)[pdof[4]]
	   + 0.5 * ((*drv)[pdof[6]] + (*drv)[pdof[8]]));
	
1260
      }
1261
    }
1262
1263
1264
1265
1266
1267
1268
    return;
  }

  void Lagrange::refineInter3_1d(DOFIndexed<double> *drv, 
				 RCNeighbourList* list, 
				 int n, BasisFunction* basFct)
  {
1269
    FUNCNAME("Lagrange::refineInter3_1d()");
1270

1271
1272
    if (n < 1) 
      return;
1273

1274
1275
    Element *el = list->getElement(0);
    const DOFAdmin *admin = drv->getFESpace()->getAdmin();
1276

1277
    DegreeOfFreedom *pdof = GET_MEMORY(DegreeOfFreedom, basFct->getNumber());
1278
1279
1280
1281
1282
    basFct->getLocalIndices(el, admin, pdof);
  
    /****************************************************************************/
    /*  values on child[0]                                                      */
    /****************************************************************************/
1283
    const DegreeOfFreedom *cdof = basFct->getLocalIndices(el->getChild(0), admin, NULL);
1284
1285

    (*drv)[cdof[2]] = 
1286
1287
      (-0.0625 * ((*drv)[pdof[0]] + (*drv)[pdof[1]]) 
       + 0.5625 * ((*drv)[pdof[7]] + (*drv)[pdof[8]]));
1288
    (*drv)[cdof[3]] = 
1289
1290
1291
1292
      (0.3125 * ((*drv)[pdof[0]] - (*drv)[pdof[8]]) + 0.0625 * (*drv)[pdof[1]]
       + 0.9375 * (*drv)[pdof[7]]);
    (*drv)[cdof[4]] = (*drv)[pdof[7]];
    (*drv)[cdof[5]] = (*drv)[pdof[9]];
1293
    (*drv)[cdof[6]] =  
1294
1295
1296
1297
      (0.0625 * ((*drv)[pdof[0]] + (*drv)[pdof[1]])
       - 0.25 * ((*drv)[pdof[3]] + (*drv)[pdof[6]])
       + 0.5 * ((*drv)[pdof[4]] + (*drv)[pdof[5]] + (*drv)[pdof[9]])
       - 0.0625 * ((*drv)[pdof[7]] + (*drv)[pdof[8]]));
1298
    (*drv)[cdof[9]] = 
1299
1300
1301
      (0.0625 * (-(*drv)[pdof[0]] + (*drv)[pdof[1]]) - 0.125 * (*drv)[pdof[3]]
       + 0.375 * (*drv)[pdof[6]] + 0.1875 * ((*drv)[pdof[7]] - (*drv)[pdof[8]])
       + 0.75 * (*drv)[pdof[9]]);
1302
1303
1304
1305
1306
1307
1308
1309
1310
  
    /****************************************************************************/
    /*  values on child[1]                                                      */
    /****************************************************************************/

    cdof = basFct->getLocalIndices(el->getChild(1), admin, NULL);

    (*drv)[cdof[5]] =  (*drv)[pdof[8]];
    (*drv)[cdof[6]] =  
1311
1312
      (0.0625 * (*drv)[pdof[0]] + 0.9375 * (*drv)[pdof[8]]
       + 0.3125 * ((*drv)[pdof[1]] - (*drv)[pdof[7]]));
1313
    (*drv)[cdof[9]] =  
1314
1315
1316
      (0.0625 * ((*drv)[pdof[0]] - (*drv)[pdof[1]]) + 0.375 * (*drv)[pdof[3]]
       - 0.125 * (*drv)[pdof[6]] + 0.1875 * (-(*drv)[pdof[7]] + (*drv)[pdof[8]])
       + 0.75 * (*drv)[pdof[9]]);
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335

    if (n <= 1) {
      FREE_MEMORY(pdof, DegreeOfFreedom, basFct->getNumber());
      return;
    }
    /****************************************************************************/
    /*  adjust the value on the neihgbour                                       */
    /****************************************************************************/

    el = list->getElement(1);
    basFct->getLocalIndices(el, admin, pdof);

    /****************************************************************************/
    /*  values on neigh's child[0]                                              */
    /****************************************************************************/
    cdof = basFct->getLocalIndices(el->getChild(0), admin, NULL);
  
    (*drv)[cdof[5]] =  (*drv)[pdof[9]];
    (*drv)[cdof[6]] = 
1336
1337
1338
1339
      (0.0625 * ((*drv)[pdof[0]] + (*drv)[pdof[1]]) 
       - 0.25 * ((*drv)[pdof[3]] + (*drv)[pdof[6]])
       + 0.5 * ((*drv)[pdof[4]] + (*drv)[pdof[5]] + (*drv)[pdof[9]])
       - 0.0625 * ((*drv)[pdof[7]] + (*drv)[pdof[8]]));
1340
    (*drv)[cdof[9]] = 
1341
1342
1343
      (0.0625 * (-(*drv)[pdof[0]] + (*drv)[pdof[1]]) - 0.12500 * (*drv)[pdof[3]]
       + 0.375 * (*drv)[pdof[6]] + 0.1875 * ((*drv)[pdof[7]] - (*drv)[pdof[8]])
       + 0.75 * (*drv)[pdof[9]]);
1344
1345
1346
1347
    /****************************************************************************/
    /*  (*drv)alues on neigh's child[0]                                         */
    /****************************************************************************/

1348
1349
1350
    int node = drv->getFESpace()->getMesh()->getNode(CENTER);  
    int n0 = admin->getNumberOfPreDOFs(CENTER);
    int dof9 = el->getChild(1)->getDOF(node, n0);
1351
1352

    (*drv)[dof9] =  
1353
1354
1355
      (0.0625 * ((*drv)[pdof[0]] - (*drv)[pdof[1]]) +  0.375 * (*drv)[pdof[3]]
       - 0.125 * (*drv)[pdof[6]] + 0.1875 * (-(*drv)[pdof[7]] + (*drv)[pdof[8]])
       + 0.75  *(*drv)[pdof[9]]);
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365

    FREE_MEMORY(pdof, DegreeOfFreedom, basFct->getNumber());
    return;
  }

  void Lagrange::refineInter3_2d(DOFIndexed<double> *drv, 
				 RCNeighbourList* list, 
				 int n, 
				 BasisFunction* basFct)
  {
1366
    FUNCNAME("Lagrange::refineInter3_2d()");
1367

1368
1369
1370
1371
1372
    if (n < 1) 
      return;
    
    Element *el = list->getElement(0);
    const DOFAdmin *admin = drv->getFESpace()->getAdmin();
1373

1374
    DegreeOfFreedom pdof[10];
1375
1376
1377
1378
1379
    basFct->getLocalIndices(el, admin, pdof);
  
    /****************************************************************************/
    /*  values on child[0]                                                      */
    /****************************************************************************/
1380
    const DegreeOfFreedom *cdof = basFct->getLocalIndices(el->getChild(0), admin, NULL);
1381
1382

    (*drv)[cdof[2]] =
1383
1384
      (-0.0625 * ((*drv)[pdof[0]] + (*drv)[pdof[1]]) 
       + 0.5625 * ((*drv)[pdof[7]] + (*drv)[pdof[8]]));
1385
    (*drv)[cdof[3]] = 
1386
1387
1388
1389
      (0.3125 * ((*drv)[pdof[0]] - (*drv)[pdof[8]]) + 0.0625 * (*drv)[pdof[1]]
       + 0.9375 * (*drv)[pdof[7]]);
    (*drv)[cdof[4]] = (*drv)[pdof[7]];
    (*drv)[cdof[5]] = (*drv)[pdof[9]];
1390
    (*drv)[cdof[6]] =  
1391
1392
1393
1394
      (0.0625 * ((*drv)[pdof[0]] + (*drv)[pdof[1]])
       - 0.25 * ((*drv)[pdof[3]] + (*drv)[pdof[6]])
       + 0.5 * ((*drv)[pdof[4]] + (*drv)[pdof[5]] + (*drv)[pdof[9]])
       - 0.0625 * ((*drv)[pdof[7]] + (*drv)[pdof[8]]));
1395
    (*drv)[cdof[9]] = 
1396
1397
1398
      (0.0625 * (-(*drv)[pdof[0]] + (*drv)[pdof[1]]) - 0.125 * (*drv)[pdof[3]]
       + 0.375 * (*drv)[pdof[6]] + 0.1875 * ((*drv)[pdof[7]] - (*drv)[pdof[8]])
       + 0.75 * (*drv)[pdof[9]]);
1399
1400
1401
1402
1403
1404
1405

    /****************************************************************************/
    /*  values on child[0]                                                      */
    /****************************************************************************/

    cdof = basFct->getLocalIndices(el->getChild(1), admin, NULL);

1406
    (*drv)[cdof[5]] = (*drv)[pdof[8]];
1407
    (*drv)[cdof[6]] =  
1408
1409
      (0.0625 * (*drv)[pdof[0]] + 0.9375 * (*drv)[pdof[8]]
       + 0.3125 * ((*drv)[pdof[1]] - (*drv)[pdof[7]]));
1410
    (*drv)[cdof[9]] =  
1411
1412
1413
      (0.0625 * ((*drv)[pdof[0]] - (*drv)[pdof[1]]) + 0.375 * (*drv)[pdof[3]]
       - 0.125 * (*drv)[pdof[6]] + 0.1875 * (-(*drv)[pdof[7]] + (*drv)[pdof[8]])
       + 0.75 * (*drv)[pdof[9]]);
1414

1415
1416
    if (n <= 1)
      return;
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431

    /****************************************************************************/
    /*  adjust the value on the neihgbour                                       */
    /****************************************************************************/

    el = list->getElement(1);
    basFct->getLocalIndices(el, admin, pdof);

    /****************************************************************************/
    /*  values on neigh's child[0]                                              */
    /****************************************************************************/
    cdof = basFct->getLocalIndices(el->getChild(0), admin, NULL);
  
    (*drv)[cdof[5]] =  (*drv)[pdof[9]];
    (*drv)[cdof[6]] =  
1432
1433
1434
1435
      (0.0625 * ((*drv)[pdof[0]] + (*drv)[pdof[1]]) 
       - 0.25 * ((*drv)[pdof[3]] + (*drv)[pdof[6]])
       + 0.5 * ((*drv)[pdof[4]] + (*drv)[pdof[5]] + (*drv)[pdof[9]])
       - 0.0625 * ((*drv)[pdof[7]] + (*drv)[pdof[8]]));
1436
    (*drv)[cdof[9]] = 
1437
1438
1439
      (0.0625 * (-(*drv)[pdof[0]] + (*drv)[pdof[1]]) - 0.12500 * (*drv)[pdof[3]]
       + 0.375 * (*drv)[pdof[6]] + 0.1875 * ((*drv)[pdof[7]] - (*drv)[pdof[8]])
       + 0.75 * (*drv)[pdof[9]]);
1440
1441