Error Estimates for the Finite Volume Element Method for Elliptic PDE's in Nonconvex Polygonal Domains

Abstract

We consider standard finite volume piecewise linear approximations for second order elliptic boundary value problems on a nonconvex polygonal domain. Based on sharp shift estimates, we derive error estimations in H --, L 2 -- and L# --norm, taking into consideration the regularity of the data. Numerical experiments and counterexamples illustrate the theoretical results