diff --git a/dune/fem-dg/examples/advdiff/problems/pulse.hh b/dune/fem-dg/examples/advdiff/problems/pulse.hh index f2a5ba94c6682749425884acd7f235874404326d..981ea314c73ca0db1a5cda9085135369b2472845 100644 --- a/dune/fem-dg/examples/advdiff/problems/pulse.hh +++ b/dune/fem-dg/examples/advdiff/problems/pulse.hh @@ -14,29 +14,12 @@ namespace Fem { /** - * \brief describes the initial and exact solution of the advection-diffusion model - * for given constant velocity vector v=(v1,v2) + * \brief Describes 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>