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An Iterative Two-Grid Method for Strongly Nonlinear Elliptic Boundary Value Problems

An Iterative Two-Grid Method for Strongly Nonlinear Elliptic Boundary Value Problems

Year:    2025

Author:    Jiajun Zhan, Lei Yang, Xiaoqing Xing, Liuqiang Zhong

Journal of Computational Mathematics, Vol. 43 (2025), Iss. 3 : pp. 673–689

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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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2305-m2023-0088

Journal of Computational Mathematics, Vol. 43 (2025), Iss. 3 : pp. 673–689

Published online:    2025-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Iterative two-grid method Convergence Strongly nonlinear elliptic problems.

Author Details

Jiajun Zhan

Lei Yang

Xiaoqing Xing

Liuqiang Zhong