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]) {
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	delete (*bary)[i];
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	(*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);
      } 
    }

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    Lagrange* newLagrange = new Lagrange(dim, degree);
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    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) {
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	delete *it;
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	*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
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	    phiDimDegree[dim][degree].push_back(new Phi(this, 
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							INDEX_OF_DIM(i ,dim),j, k));
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	    // gradients
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	    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
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	    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() { 
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    delete [] vertices; 
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  }
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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() { 
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    delete [] vertices; 
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  }
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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() { 
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    delete [] vertices; 
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  }
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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) {
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      vec = new DimVec<double>(dim, DEFAULT_VALUE, 0.0);
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    }
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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);
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      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());
  }


  // ===== 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];
  }

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  void Lagrange::refineInter1(DOFIndexed<double> *drv, RCNeighbourList* list, int n, 
			      BasisFunction* basFct)
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  {
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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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  }

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  void Lagrange::refineInter2_1d(DOFIndexed<double> *drv, RCNeighbourList* list, int n, 
				 BasisFunction* basFct)
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  {
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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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    /****************************************************************************/
    /*  midpoint of edge on child[1] at the refinement edge                     */
    /****************************************************************************/
  
    cdof = el->getChild(1)->getDOF(node, n0); 
    (*drv)[cdof] = 
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  }

  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]]);
    }
1179
1180
1181
1182
1183
1184
  }

  void Lagrange::refineInter2_3d(DOFIndexed<double> *drv, 
				 RCNeighbourList* list, 
				 int n, BasisFunction* basFct)
  {
1185
    FUNCNAME("Lagrange::refineInter2_3d()");
1186

1187
1188
    if (n < 1) 
      return;
1189

1190
1191
    Element *el = list->getElement(0);
    const DOFAdmin *admin = drv->getFESpace()->getAdmin();
1192

1193
    DegreeOfFreedom pdof[10];
1194
1195
    basFct->getLocalIndices(el, admin, pdof);

1196
1197
    int node0 = drv->getFESpace()->getMesh()->getNode(EDGE);
    int n0 = admin->getNumberOfPreDOFs(EDGE);
1198
1199
1200
1201
1202

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

1203
    const DegreeOfFreedom *cdof = basFct->getLocalIndices(el->getChild(0), admin, NULL);
1204
1205
1206

    (*drv)[cdof[3]] = ((*drv)[pdof[4]]);
    (*drv)[cdof[6]] = 
1207
1208
      (0.375 * (*drv)[pdof[0]] - 0.125 * (*drv)[pdof[1]] 
       + 0.75 * (*drv)[pdof[4]]);
1209
    (*drv)[cdof[8]] = 
1210
1211
      (0.125 * (-(*drv)[pdof[0]] - (*drv)[pdof[1]]) + 0.25 * (*drv)[pdof[4]]
       + 0.5 * ((*drv)[pdof[5]] + (*drv)[pdof[7]]));
1212
    (*drv)[cdof[9]] = 
1213
1214
      (0.125 * (-(*drv)[pdof[0]] - (*drv)[pdof[1]]) + 0.25 * (*drv)[pdof[4]]
       + 0.5 * ((*drv)[pdof[6]] + (*drv)[pdof[8]]));
1215
1216
1217
1218
1219

    /****************************************************************************/
    /*  values on child[1]                                                      */
    /****************************************************************************/
  
1220
    DegreeOfFreedom cdofi = el->getChild(1)->getDOF(node0 + 2, n0);
1221
    (*drv)[cdofi] = 
1222
1223
      (-0.125 * (*drv)[pdof[0]] + 0.375 * (*drv)[pdof[1]] 
       + 0.75 * (*drv)[pdof[4]]);
1224
1225
1226
1227
1228

    /****************************************************************************/
    /*   adjust neighbour values                                                */
    /****************************************************************************/
  
1229
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
    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]]));
	
1259
      }
1260
    }
1261
1262
1263
1264
1265
1266
  }

  void Lagrange::refineInter3_1d(DOFIndexed<double> *drv, 
				 RCNeighbourList* list, 
				 int n, BasisFunction* basFct)
  {
1267
    FUNCNAME("Lagrange::refineInter3_1d()");
1268

1269
1270
    if (n < 1) 
      return;
1271

1272
1273
    Element *el = list->getElement(0);
    const DOFAdmin *admin = drv->getFESpace()->getAdmin();
1274

1275
    DegreeOfFreedom *pdof = GET_MEMORY(DegreeOfFreedom, basFct->getNumber());
1276
1277
1278
1279
1280
    basFct->getLocalIndices(el, admin, pdof);
  
    /****************************************************************************/
    /*  values on child[0]                                                      */
    /****************************************************************************/
1281
    const DegreeOfFreedom *cdof = basFct->getLocalIndices(el->getChild(0), admin, NULL);
1282
1283

    (*drv)[cdof[2]] = 
1284
1285
      (-0.0625 * ((*drv)[pdof[0]] + (*drv)[pdof[1]]) 
       + 0.5625 * ((*drv)[pdof[7]] + (*drv)[pdof[8]]));
1286
    (*drv)[cdof[3]] = 
1287
1288
1289
1290
      (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]];
1291
    (*drv)[cdof[6]] =  
1292
1293
1294
1295
      (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]]));
1296
    (*drv)[cdof[9]] = 
1297
1298
1299
      (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]]);
1300
1301
1302
1303
1304
1305
1306
1307
1308
  
    /****************************************************************************/
    /*  values on child[1]                                                      */
    /****************************************************************************/

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

    (*drv)[cdof[5]] =  (*drv)[pdof[8]];
    (*drv)[cdof[6]] =  
1309
1310
      (0.0625 * (*drv)[pdof[0]] + 0.9375 * (*drv)[pdof[8]]
       + 0.3125 * ((*drv)[pdof[1]] - (*drv)[pdof[7]]));
1311
    (*drv)[cdof[9]] =  
1312
1313
1314
      (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]]);
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333

    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]] = 
1334
1335
1336
1337
      (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]]));
1338
    (*drv)[cdof[9]] = 
1339
1340
1341
      (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]]);
1342
1343
1344
1345
    /****************************************************************************/
    /*  (*drv)alues on neigh's child[0]                                         */
    /****************************************************************************/

1346
1347
1348
    int node = drv->getFESpace()->getMesh()->getNode(CENTER);  
    int n0 = admin->getNumberOfPreDOFs(CENTER);
    int dof9 = el->getChild(1)->getDOF(node, n0);
1349
1350

    (*drv)[dof9] =  
1351
1352
1353
      (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]]);
1354
1355
1356
1357
1358
1359
1360
1361
1362

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

  void Lagrange::refineInter3_2d(DOFIndexed<double> *drv, 
				 RCNeighbourList* list, 
				 int n, 
				 BasisFunction* basFct)
  {
1363
    FUNCNAME("Lagrange::refineInter3_2d()");
1364

1365
1366
1367
1368
1369
    if (n < 1) 
      return;
    
    Element *el = list->getElement(0);
    const DOFAdmin *admin = drv->getFESpace()->getAdmin();
1370

1371
    DegreeOfFreedom pdof[10];
1372
1373
1374
1375
1376
    basFct->getLocalIndices(el, admin, pdof);
  
    /****************************************************************************/
    /*  values on child[0]                                                      */
    /****************************************************************************/
1377
    const DegreeOfFreedom *cdof = basFct->getLocalIndices(el->getChild(0), admin, NULL);
1378
1379

    (*drv)[cdof[2]] =
1380
1381
      (-0.0625 * ((*drv)[pdof[0]] + (*drv)[pdof[1]]) 
       + 0.5625 * ((*drv)[pdof[7]] + (*drv)[pdof[8]]));
1382
    (*drv)[cdof[3]] = 
1383
1384
1385
1386
      (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]];
1387
    (*drv)[cdof[6]] =  
1388
1389
1390
1391
      (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]]));