Some refined Finite volume methods for elliptic problems with corner singularities
Résumé
It is well known that the solution of the Laplace equation in a non convex
polygonal domain of $R^2$ has a singular behaviour near non convex corners.
Consequently we investigate three refined finite volume methods (cell-center,
conforming finite volume-element and non conforming finite volume-element)
to approximate the solution of such a problem and restore optimal orders
of convergence as for smooth solutions. Numerical tests are presented and
confirm the theoretical rates of convergence.
Domaines
Analyse numérique [math.NA]
Origine : Fichiers produits par l'(les) auteur(s)