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An Iterative Two-Grid Method for Strongly Nonlinear Elliptic Boundary Value Problems
Jiajun Zhan, Lei Yang, Xiaoqing Xing and Liuqiang Zhong

J. Comp. Math. DOI: 10.4208/jcm.2305-m2023-0088

Publication Date : 2024-04-12

  • Abstract

We design and analyze an iterative two-grid algorithm for the finite element discretizations of strongly nonlinear elliptic boundary value problems in this paper. We propose an iterative two-grid algorithm, in which a nonlinear problem is first solved on the coarse space, and then a symmetric positive definite problem is solved on the fine space. The main contribution in this paper is to establish a first convergence analysis, which requires dealing with four coupled error estimates, for the iterative two-grid methods. We also present some numerical experiments to confirm the efficiency of the proposed algorithm.

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