Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems

被引：47

作者：

Wu Haijun ^{[1
]}

Chen Zhiming ^{[1
]}

机构：

[1] Chinese Acad Sci, Inst Computat Math, Beijing 100080, Peoples R China

来源：

SCIENCE IN CHINA SERIES A-MATHEMATICS | 2006年 / 49卷 / 10期

基金：

中国国家自然科学基金;

关键词：

multigrid V-cycle algorithm; adaptive finite element meshes; local relaxation; Scott-Zhang interpolation;

D O I：

10.1007/s11425-006-2005-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we prove the uniform convergence of the standard multigrid V-cycle algorithm with the Gauss-Seidel relaxation performed only on the new nodes and their "immediate" neighbors for discrete elliptic problems on the adaptively refined finite element meshes using the newest vertex bisection algorithm. The proof depends on sharp estimates on the relationship of local mesh sizes and a new stability estimate for the space decomposition based on the Scott-Zhang interpolation operator. Extensive numerical results are reported, which confirm the theoretical analysis.

引用

页码：1405 / 1429

页数：25

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