Convergence of the multigrid V-cycle algorithm for second-order boundary value problems without full elliptic regularity

被引：0

作者：

Brenner, SC ^{[1
]}

机构：

[1] Univ S Carolina, Dept Math, Columbia, SC 29208 USA

来源：

MATHEMATICS OF COMPUTATION | 2002年 / 71卷 / 238期

关键词：

V-cycle multigrid algorithm; second-order boundary value problems without full elliptic regularity;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The multigrid V-cycle algorithm using the Richardson relaxation scheme as the smoother is studied in this paper. For second-order elliptic boundary value problems, the contraction number of the V-cycle algorithm is shown to improve uniformly with the increase of the number of smoothing steps, without assuming full elliptic regularity. As a consequence, the V-cycle convergence result of Braess and Hackbusch is generalized to problems without full elliptic regularity.

引用

页码：507 / 525

页数：19

共 50 条

[1] Convergence of nonconforming V-cycle and F-cycle multigrid algorithms for second order elliptic boundary value problems
Brenner, SC
MATHEMATICS OF COMPUTATION, 2004, 73 (247) : 1041 - 1066
[2] On the convergence of the nonnested V-cycle multigrid method for nonsymmetric and indefinite second-order elliptic problems
ICMSEC, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China
J Comput Math, 2006, 2 (157-168):
[3] On the convergence of the nonnested V-cycle multigrid method for nonsymmetric and indefinite second-order elliptic problems
Duan, HY
Lin, Q
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2006, 24 (02) : 157 - 168
[4] Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems
Wu Haijun
Chen Zhiming
SCIENCE IN CHINA SERIES A-MATHEMATICS, 2006, 49 (10): : 1405 - 1429
[5] Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems
WU Haijun & CHEN Zhiming Institute of Computational Mathematics
Science in China(Series A:Mathematics), 2006, (10) : 1405 - 1429
[6] Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems
Haijun Wu
Zhiming Chen
Science in China Series A: Mathematics, 2006, 49 : 1405 - 1429
[7] Uniform convergence of Galerkin-multigrid methods for nonconforming finite elements for second-order problems with less than full elliptic regularity
Chen, ZX
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2002, 18 (02) : 203 - 217
[8] Convergence analysis of V-Cycle multigrid methods for anisotropic elliptic equations
Wu, Yongke
Chen, Long
Xie, Xiaoping
Xu, Jinchao
IMA JOURNAL OF NUMERICAL ANALYSIS, 2012, 32 (04) : 1329 - 1347
[9] Convergence of nonconforming multigrid methods without full elliptic regularity
Brenner, SC
MATHEMATICS OF COMPUTATION, 1999, 68 (225) : 25 - 53
[10] A Fourier Transform Analysis of Convergence Properties of Multigrid V-Cycle Algorithm
Zhang, Y.
Li, M.
Liu, G. R.
INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, 2019, 16 (04)

← 1 2 3 4 5 →