GLOBAL AND LOCAL POINTWISE ERROR ESTIMATES FOR FINITE ELEMENT APPROXIMATIONS TO THE STOKES PROBLEM ON CONVEX POLYHEDRA

被引：3

作者：

Behringer, Niklas ^{[1
]}

Leykekhman, Dmitriy ^{[2
]}

Vexler, Boris ^{[1
]}

机构：

[1] Tech Univ Munich, Ctr Math Sci, Chair Optimal Control, D-85748 Garching, Germany

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

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2020年 / 58卷 / 03期

基金：

美国国家科学基金会; 奥地利科学基金会;

关键词：

maximum norm; finite element; best approximation error estimates; Stokes; NORM STABILITY; L-INFINITY; OPERATOR;

D O I：

10.1137/19M1274456

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main goal of the paper is to show new stability and localization results for the finite element solution of the Stokes system in W-1,W-infinity and L-infinity norms under standard assumptions on the finite element spaces on quasi-uniform meshes in two and three dimensions. Although interior error estimates are well-developed for the elliptic problem, they appear to be new for the Stokes system on unstructured meshes. To obtain these results we extend previously known stability estimates for the Stokes system using regularized Green's functions.

引用

页码：1531 / 1555

页数：25

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