Two-grid weak Galerkin method for semilinear elliptic differential equations

被引:1
|
作者
Chen, Luoping [1 ]
Wu, Fanyun [1 ]
Zeng, Guoyan [1 ]
机构
[1] Southwest Jiaotong Univ, Sch Math, Chengdu 611756, Sichuan, Peoples R China
基金
中国国家自然科学基金;
关键词
semilinear elliptic differential equations; two-grid discretization; weak Galerkin method; FINITE-ELEMENT-METHOD; SCHEME;
D O I
10.1002/mma.8519
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we investigate a two-grid weak Galerkin method for semilinear elliptic differential equations. The method mainly contains two steps. First, we solve the semilinear elliptic equation on the coarse mesh with mesh size H$$ H $$, then, we use the coarse mesh solution as an initial guess to linearize the semilinear equation on the fine mesh, that is, on the fine mesh (with mesh size h$$ h $$), we only need to solve a linearized system. Theoretical analysis shows that when the exact solution u$$ u $$ has sufficient regularity and h=H2$$ h={H}<^>2 $$, the two-grid weak Galerkin method achieves the same convergence accuracy as weak Galerkin method. Several examples are given to verify the theoretical results.
引用
收藏
页码:423 / 437
页数:15
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