Commit 645e6786 by Praetorius, Simon

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

parent 38651101
 ... ... @@ -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(...) 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 \ No newline at end of file \ No newline at end of file
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