New answers tagged pde
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Should reaction be taken into account in the CFL condition when solving advection-diffusion-reaction equations numerically?
The CFL criterion is derived for convective problems usually. You may also get a similar criterion for diffusion problems (although the grid size is squared in the formula).
For the reaction however, ...
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Should reaction be taken into account in the CFL condition when solving advection-diffusion-reaction equations numerically?
The CFL condition refers strictly to purely hyperbolic problems where there is a well-defined domain of dependence for the analytical solution. It state that a necessary condition for stability is ...
- 814
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What FEM solver should be used for matrix-valued FE spaces?
This is a fairly standard elliptic problem (the operator is of the form $-\Delta - \text{grad}\,\text{div}$). It is vector-valued (in fact matrix-valued) in the same way as the elasticity equations ...
- 50.7k
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Should reaction be taken into account in the CFL condition when solving advection-diffusion-reaction equations numerically?
CFL is a necessary requirement for stability in transport-dominated systems, but in practice, is an intuitive way to interpret linear stability. A 1D advection-diffusion (or somewhat upwinded ...
- 25.3k
8
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Accepted
A priori FEM estimates without $H^2$ regularity
The usual argument for error estimates in the energy norm is to first use the best-approximation property to get things back to the interpolation error. That is,
$$
\| u-u_h \|_{H^1} \le C \| u-u_I \...
- 50.7k
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