Some refined Finite volume methods for elliptic problems with corner singularities

Abstract :

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.

Date of publication: October 2003

paper presented by : Professor Raphaele Herbin