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

Abstract

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 Hölder estimates for the corresponding Green’s function are obtained. As an applications of these estimates to finite element methods, we show the best approximation property of the error in W 1 ∞. In… (More)
DOI: 10.1007/s00211-009-0213-y

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Cite this paper

@article{Guzmn2009HlderEF, title={H{\"{o}lder estimates for Green's functions on convex polyhedral domains and their applications to finite element methods}, author={Johnny Guzm{\'a}n and Dmitriy Leykekhman and J{\"{u}rgen Ro\ssmann and Alfred H. Schatz}, journal={Numerische Mathematik}, year={2009}, volume={112}, pages={221-243} }