# Tag Info

### 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

### 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

### 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
### 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 \...