Skip to content

[example][bugfix] Change sign of flux in poisson-mfem

Carsten Gräser requested to merge bugfix/fix-poisson-mfem-bc into master

Starting from the Poisson equation -\Delta u = f and setting \sigma = \nabla u (or \sigma - \nabla u =0) we obtain \nabla \cdot \sigma = -f. Using partial integration we obtain the weak form \int \sigma \cdot \tau + u \nabla \cdot \tau= 0 of the flux equation. Thus the combined weak formulations reads:

\int \sigma \cdot \tau + u \nabla \cdot \tau + (\nabla \cdot \sigma)v = \int -fv.

So far the example contained a minus sign in front of both flux-pressure terms. This corresponds to defining \sigma to be the negative flux \sigma = -\nabla u. Hence the essential boundary condition for \sigma was in fact a negative flux BC. Maybe this was on purpose but I cannot see any reason for this.

This MR changes the sign, such that the essential BC for \sigma corresponds to a Neumann BC for u.

It also modifies the boundary values and rhs of the example, because the previous ones where so small that one could not see the sign error.

Merge request reports