TWO-GRID WEAK GALERKIN METHOD FOR SEMILINEAR ELLIPTIC DIFFERENTIAL EQUATIONS
• luoping chen,
• fanyun wu,
• guoyan zeng
luoping chen
Southwest Jiaotong University
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fanyun wu
Southwest Jiaotong University
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guoyan zeng
Southwest Jiaotong University
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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 semi-linear elliptic equation on the coarse mesh with mesh size H, then, we use the coarse mesh solution as a initial guess to linearize the semilinear equation on the fine mesh, i.e., on the fine mesh (with mesh size $h$), we only need to solve a linearized system. Theoretical analysis shows that when the exact solution u has sufficient regularity and $h=H^2$, the two-grid weak Galerkin method achieves the same convergence accuracy as weak Galerkin method. Several examples are given to verify the theoretical results.

Peer review status:UNDER REVIEW

06 Jan 2022Submitted to Mathematical Methods in the Applied Sciences
07 Jan 2022Assigned to Editor
07 Jan 2022Submission Checks Completed
14 Jan 2022Reviewer(s) Assigned