COMPUTATION OF THE LBB CONSTANT FOR THE STOKES EQUATION WITH A LEAST-SQUARES FINITE ELEMENT METHOD

被引：2
|
作者：
Storn, Johannes [1 ]
机构：
[1] Bielefeld Univ, Dept Math, D-33615 Bielefeld, Germany
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2020年 / 58卷 / 01期
关键词：
LBB constant; LSFEM; Cosserat spectrum; ellipticity constants; upper eigenvalue bounds; noncompact eigenvalue problem; Stokes problem; INF-SUP CONSTANT; DIVERGENCE OPERATOR; PSEUDOSTRESS APPROXIMATION; RIGHT INVERSE; INEQUALITIES; FORMULATION; FRIEDRICHS; FLOW; CONTINUITY; EXISTENCE;
D O I：
10.1137/18M1231183
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An investigation of a least-squares finite element method (LSFEM) for the Stokes equation reveals a relation of the Ladyzhenslaya-Babugka-Brezzi (LBB) constant and the ellipticity constants of the LSFEM. While the approximation of the LBB constant with standard numerical methods is challenging, the approximation of the ellipticity constants is in a Rayleigh-Ritz-like environment. This setting is well understood and so allows for an easy-to-implement convergent numerical scheme for the computation of the LBB constant. Numerical experiments with uniform and adaptive mash refinements complement the investigation of this novel scheme.
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页码：86 / 108
页数：23
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