ROBUST PRECONDITIONING ESTIMATES FOR CONVECTION-DOMINATED ELLIPTIC PROBLEMS VIA A STREAMLINE POINCARE-FRIEDRICHS INEQUALITY

被引：2

作者：

Axelsson, Owe ^{[1
]}

Karatson, Janos ^{[2
,3
,4
]}

Kovacs, Balazs ^{[2
,3
]}

机构：

[1] Inst Geon AS CR, Innovat IT4, Ostrava, Czech Republic

[2] ELTE Univ, Dept Appl Anal, H-1518 Budapest, Hungary

[3] ELTE Univ, MTA ELTE NumNet Res Grp, H-1518 Budapest, Hungary

[4] Tech Univ Budapest, Dept Anal, Budapest, Hungary

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2014年 / 52卷 / 06期

基金：

匈牙利科学研究基金会;

关键词：

streamline diffusion finite element method; robust preconditioning; Poincare-Friedrichs inequality; ITERATIVE METHODS; NONSYMMETRIC SYSTEMS; CONJUGATE-GRADIENT; DIFFUSION PROBLEMS; LINEAR-EQUATIONS;

D O I：

10.1137/130940268

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to the streamline diffusion finite element method, combined with equivalent preconditioning, for solving convection-dominated elliptic problems. The preconditioner is obtained from the streamline diffusion inner product. It is proved that the obtained convergence is robust, i.e., bounded independently of the perturbation parameter e, for proper convection vector fields. The key to the estimates is an improved "streamline" Poincare-Friedrichs inequality.

引用

页码：2957 / 2976

页数：20

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