Error estimates for a finite volume element method for elliptic PDES in nonconvex polygonal domains

摘要

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-1-, L-2- and L-infinity-norms, taking into consideration the regularity of the data. Numerical experiments and counterexamples illustrate the theoretical results.