Multilevel correction adaptive finite element method for semilinear elliptic equation

被引：0
作者：
Qun Lin
Hehu Xie
Fei Xu
机构：
[1] Chinese Academy of Sciences No. 55,LSEC, Academy of Mathematics and Systems Science
来源：
Applications of Mathematics | 2015年 / 60卷
关键词：
semilinear elliptic problem; multilevel correction; adaptive finite element method; 65N30; 35J61; 65B99; 62F35;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A type of adaptive finite element method is presented for semilinear elliptic problems based on multilevel correction scheme. The main idea of the method is to transform the semilinear elliptic equation into a sequence of linearized boundary value problems on the adaptive partitions and some semilinear elliptic problems on very low dimensional finite element spaces. Hence, solving the semilinear elliptic problem can reach almost the same efficiency as the adaptive method for the associated boundary value problem. The convergence and optimal complexity of the new scheme can be derived theoretically and demonstrated numerically.
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页码：527 / 550
页数：23
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