Two‐grid weak Galerkin method for semilinear elliptic differential equations. (25th June 2022)

• Record Type: Journal Article
• Authors: Chen, Luoping; Wu, Fanyun; Zeng, Guoyan
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 1(2023)
• Page Start: 423
• Page End: 437
• Publication Date: 2022-06-25
• Subjects: semilinear elliptic differential equations -- two‐grid discretization -- weak Galerkin method; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8519
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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 = H 2 $$ h={H}^2 $$, the two‐grid weak Galerkin method achieves the same convergence accuracy as weak Galerkin method. Several examples are given to verify the theoretical results.