A full multigrid method for semilinear elliptic equation

被引：0
作者：
Fei Xu
Hehu Xie
机构：
[1] Beijing University of Technology,Beijing Institute for Scientific and Engineering Computing
[2] Chinese Academy of Sciences,LSEC, Academy of Mathematics and Systems Science
[3] University of Chinese Academy of Sciences,School of Mathematical Sciences
来源：
Applications of Mathematics | 2017年 / 62卷
关键词：
semilinear elliptic problem; full multigrid method; multilevel correction; finite element method; 65N30; 65N25; 65L15; 65B99;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and semilinear problems on a very low dimensional space. The linearized boundary value problems are solved by some multigrid iterations. Besides the multigrid iteration, all other efficient numerical methods can also serve as the linear solver for solving boundary value problems. The optimality of the computational work is also proved. Compared with the existing multigrid methods which need the bounded second order derivatives of the nonlinear term, the proposed method only needs the Lipschitz continuation in some sense of the nonlinear term.
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页码：225 / 241
页数：16
相关论文
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