update the links and some latex in the navier-stokes example

docs/examples/navier-stokes.md

@@ -15,7 +15,7 @@ Discretization
 --------------
 
 ### Weak formulation
-In a weak variational formulation, we try to find $`\mathbf{u}(t,\cdot)\in \mathbf{V}_\mathbf{g}:=\{\mathbf{v}\in H^1(\Omega)^d\,:\, \operatorname{tr}_{\partial\Omega}\mathbf{v} = \mathbf{g}\}`$ and $`p(t,\cdot)\in Q:=L^2(\Omega)`$, such that
+In a weak variational formulation, we try to find $`\mathbf{u}(t,\cdot)\in \mathbf{V}_\mathbf{g}:=\{\mathbf{v}\in H^1(\Omega)^d\,:\, \operatorname{tr}_{\partial\Omega}\mathbf{v} = \mathbf{g}\}`$ and $`p(t,\cdot)\in Q:=L_0^2(\Omega)`$, such that
 ```math
 \int_\Omega \varrho(\partial_t\mathbf{u} + (\mathbf{u}\cdot\nabla)\mathbf{u})\cdot\mathbf{v} + \nu\nabla\mathbf{u}:\nabla\mathbf{v} + p\,\nabla\cdot\mathbf{v}\,\text{d}\mathbf{x} = \int_\Omega \mathbf{f}\cdot\mathbf{v}\,\text{d}\mathbf{x},\qquad\forall \mathbf{v}\in \mathbf{V}_0, \\
 \int_\Omega q\,\nabla\cdot\mathbf{u}\,\text{d}\mathbf{x} = 0,\qquad \forall q\in Q.
@@ -50,7 +50,7 @@ auto basis = composite(
       lagrange<1>(), flatLexicographic());
 ```
 At this point, any Dirichlet boundary conditions are ignored in the definition of the bases. We
-build the Taylor-Hood basis as a composition of a product of $`d`$ $`\mathbb{V}_2`$ bases for
+build the Taylor-Hood basis as a composition of a product of $`d\times\mathbb{V}_2`$ bases for
 the velocity components and a $`\mathbb{V}_1`$ basis for the pressure. We have to use
 `composite(...)` to combine the different types for velocity and pressure space, while we
 can use `power<d>(...)` for the `d` velocity component spaces of the same type.
@@ -76,10 +76,10 @@ with a [`ProblemStat`](../reference/Problem.md#class-problemstat) .
 
 ```c++
 using namespace AMDiS;
-ProblemStat prob("stokes", grid, basis);
+ProblemStat prob{"stokes", grid, basis};
 prob.initialize(INIT_ALL);
 
-ProblemInstat probInstat("stokes", prob);
+ProblemInstat probInstat{"stokes", prob};
 probInstat.initialize(INIT_UH_OLD);
 ```
 For convenience, we use class template argument deduction here.
@@ -200,7 +200,7 @@ adapt.adapt();
 Complete Example
 ----------------
 The full source code of the Navier-Stokes example can be found in the repository
-at [examples/navier_stokes.cc](https://gitlab.mn.tu-dresden.de/amdis/amdis-core/blob/master/examples/navier-stokes.cpp).
+at [examples/navier_stokes.cc](https://gitlab.mn.tu-dresden.de/amdis/amdis-core/blob/master/examples/navier_stokes.cc).
 
 Compile with
 ```bash
@@ -214,4 +214,4 @@ and run with
 
 The flow field with `density=1`, `viscosity=1` and `boundary velocity=10` will look like
 
-<img src="../images/navier-stokes.png" with="50%" />
\ No newline at end of file
+<img src="../../images/navier-stokes.png" with="50%" />
\ No newline at end of file