Convergence of a positive nonlinear DDFV scheme for degenerate parabolic equations
Résumé
In this work, we carry out the convergence analysis of a positive DDFV method for approximating
solutions of degenerate parabolic equations. The basic idea rests upon different approximations of the
fluxes on the same interface of the control volume. Precisely, the approximated flux is split into two terms
corresponding to the primal and dual normal components. Then the first term is discretized using a centered
scheme whereas the second one is approximated in a non evident way by an upstream scheme. The novelty
of our approach is twofold: on the one hand we prove that the resulting scheme preserves the positivity
and on the other hand we establish energy estimates. Some numerical tests are presented and they show
that the scheme in question turns out to be robust and efficient. The accuracy is almost of second order on
general meshes when the solution is smooth.
Origine : Fichiers produits par l'(les) auteur(s)
Loading...