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arXiv · 2301.02875

An iterative two-grid method for strongly nonlinear elliptic boundary value problems

Jiajun Zhan·Lei Yang·Xiaoqing Xing·Liuqiang Zhong
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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 innovation of this paper lies in the establishment of a first convergence analysis, which requires simultaneous estimation of four interconnected error estimates. We also present some numerical experiments to confirm the efficiency of the proposed algorithm.

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Jiajun Zhan, Lei Yang, Xiaoqing Xing, Liuqiang Zhong. 2023-01-07. An iterative two-grid method for strongly nonlinear elliptic boundary value problems. https://arxiv.org/abs/2301.02875

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