Uniform Convergence of Multigrid V-Cycle on Adaptively Refined Finite Element Meshes for Elliptic Problems with Discontinuous Coefficients  

作　　者：Haijun Wu Weiying Zheng 

机构地区：[1]Department of Mathematics,Nanjing University,Jiangsu 210093,P.R.China [2]LSEC,Institute of Computational Mathematics,Academy of Mathematics and System Sciences Chinese Academy of Sciences,Beijing 100190,P.R.China

出　　处：《Communications in Mathematical Research》2023年第3期437-475,共39页数学研究通讯（英文版）

基　　金：supported by the NSF of China (Grant Nos.12171238,12261160361);supported in part by the China NSF for Distinguished Young Scholars (Grant No.11725106);by the China NSF major project (Grant No.11831016).

摘　　要：The multigrid V-cycle methods for adaptive finite element discretizations of two-dimensional elliptic problems with discontinuous coefficients are considered.Under the conditions that the coefficient is quasi-monotone up to a constant and the meshes are locally refined by using the newest vertex bisection algorithm,some uniform convergence results are proved for the standard multigrid V-cycle algorithm with Gauss-Seidel relaxations performed only on new nodes and their immediate neighbours.The multigrid V-cycle algorithm uses O(N)operations per iteration and is optimal.

关 键 词：MULTIGRID adaptive finite elements elliptic problems discontinuous coefficients uniform convergence 

分 类 号：O186.11[理学—数学]