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

被引：39

作者：

Guzman, J. ^{[2
]}

Leykekhman, D. ^{[1
]}

Rossmann, J. ^{[3
]}

Schatz, A. H. ^{[4
]}

机构：

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

[2] Brown Univ, Div Appl Math, Providence, RI 02906 USA

[3] Univ Rostock, Math Inst, D-18051 Rostock, Germany

[4] Cornell Univ, Dept Math, Ithaca, NY 14853 USA

来源：

NUMERISCHE MATHEMATIK | 2009年 / 112卷 / 02期

基金：

美国国家科学基金会;

关键词：

BOUNDARY-VALUE-PROBLEMS; DISCONTINUOUS GALERKIN METHODS; ERROR EXPANSION INEQUALITIES; 2ND-ORDER ELLIPTIC-SYSTEMS; L-INFINITY; LOCALIZED POINTWISE; DIRICHLET PROBLEM; IRREGULAR MESHES; APPROXIMATIONS; CONVERGENCE;

D O I：

10.1007/s00211-009-0213-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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 Holder 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-infinity(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.

引用

页码：221 / 243

页数：23

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