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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.
06 Jan 2022Submitted to Mathematical Methods in the Applied Sciences
07 Jan 2022Submission Checks Completed
07 Jan 2022Assigned to Editor
14 Jan 2022Reviewer(s) Assigned
14 May 2022Review(s) Completed, Editorial Evaluation Pending
16 May 2022Editorial Decision: Revise Major
10 Jun 20221st Revision Received
10 Jun 2022Submission Checks Completed
10 Jun 2022Assigned to Editor
10 Jun 2022Reviewer(s) Assigned
11 Jun 2022Review(s) Completed, Editorial Evaluation Pending
12 Jun 2022Editorial Decision: Accept
25 Jun 2022Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.8519