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dune-fem
dune-fem-dg
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a4fc75d0
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a4fc75d0
authored
9 years ago
by
Robert K
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added link to paper.
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dune/fem-dg/examples/advdiff/problems/pulse.hh
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@@ -14,29 +14,12 @@ namespace Fem
{
/**
* \brief
d
escribes the initial and exact solution of the advection-diffusion model
*
for given constant velocity vector v=(v1,v2)
* \brief
D
escribes the initial and exact solution of the advection-diffusion model
*
described in:
*
* \ingroup AdvDiffProblems
*
* \f[u(x,y,z,t):=\displaystyle{\sum_{i=0}^{1}} T_i(t) \cdot X_i(x) \cdot
* Y_i(y) \cdot Z_i(z)\f]
*
* with
*
* \f{eqnarray*}{
* T_0(t) &:=& e^{-\varepsilon t \pi^2 (2^2 + 1^2 + 1.3^2 )} \\
* X_0(x) &:=& 0.6\cdot \cos(2\pi (x-v_1t)) + 0.8\cdot \sin(2\pi (x-v_1t)) \\
* Y_0(y) &:=& 1.2\cdot \cos(1\pi (y-v_2t)) + 0.4\cdot \sin(1\pi (y-v_2t)) \\
* Z_0(z) &:=& 0.1\cdot \cos(1.3\pi (z-v_3t)) - 0.4\cdot \sin(1.3\pi (z-v_3t)) \\
* T_1(t) &:=& e^{-\varepsilon t \pi^2 (0.7^2 + 0.5^2 + 0.1^2 )} \\
* X_1(x) &:=& 0.9\cdot \cos(0.7\pi (x-v_1t)) + 0.2\cdot \sin(0.7\pi (x-v_1t)) \\
* Y_1(y) &:=& 0.3\cdot \cos(0.5\pi (y-v_2t)) + 0.1\cdot \sin(0.5\pi (y-v_2t)) \\
* Z_1(z) &:=& -0.3\cdot \cos(0.1\pi (z-v_3t)) + 0.2\cdot \sin(0.1\pi (z-v_3t))
* \f}
*
* This is a solution of the AdvectionDiffusionModel for \f$g_D = u|_{\partial
* \Omega}\f$.
* P. Bastian. Higher Order Discontinuous Galerkin Methods for Flow and Transport in Porous Media
* Challenges in Scientific Computing - CISC 2002, Volume 35 of the series
* Lecture Notes in Computational Science and Engineering pp 1-22
*
*/
template
<
class
GridType
,
int
dimRange
>
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