H_lder estimates for Green's functions on convex polyhedral domains and their applications to finite element methods

摘要

A model second-order elliptic equation on a general convex polyhedral domain in three dimensions is considered. The aim of this paper is twofold: First sharp H_lder estimates for the corresponding Green's function are obtained. As an applica_tions of these estimates to finite element methods, we show the best approximation property of the error in W__~1. In contrast to previously known results, W_p~2 regularity for p > 3, which does not hold for general convex polyhedral domains, is not required. Furthermore, the new Green's function estimates allow us to obtain localized error estimates at a point.