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

作　　者：WU Haijun CHEN Zhiming 

机构地区：[1]Department of Mathematics, Nanjing University, Nanjing 210093, China Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing 100080, China.

出　　处：《Science China Mathematics》2006年第10期1405-1429,共25页中国科学：数学（英文版）

基　　金：The first author was supported in part by the National Natural Science Foundation of China(Grant No.10401016);by the National Basic Research Program(Grant No.2005CB321701);The second author was supported in part by the National Natural Science Foundation of China(Grant No.10025102);by China MOS(Grant No.G1999032802).

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.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.

关 键 词：MULTIGRID V-CYCLE algorithm  adaptive FINITE element meshes  local relaxation  Scott-Zhang interpolation. 

分 类 号：N[自然科学总论]