full
search.png

Search

close.png

Cancel

arrow
Volume 43, Issue 3
An Iterative Two-Grid Method for Strongly Nonlinear Elliptic Boundary Value Problems

Jiajun Zhan, Lei Yang, Xiaoqing Xing & Liuqiang Zhong

DOI: 10.4208/jcm.2305-m2023-0088

J. Comp. Math., 43 (2025), pp. 673-689.

Published online: 2024-11

Preview Purchase PDF 13 131

Cited by

google scholar semantic scholar
Export citation
  • 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.

  • Keywords

Iterative two-grid method, Convergence, Strongly nonlinear elliptic problems.

  • AMS Subject Headings

65N30, 65M12, 35J60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{JCM-43-673, author = {Zhan , JiajunYang , LeiXing , Xiaoqing and Zhong , Liuqiang}, title = {An Iterative Two-Grid Method for Strongly Nonlinear Elliptic Boundary Value Problems}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {43}, number = {3}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2305-m2023-0088}, url = {http://global-sci.org/intro/article_detail/jcm/23554.html} }
TY - JOUR T1 - An Iterative Two-Grid Method for Strongly Nonlinear Elliptic Boundary Value Problems AU - Zhan , Jiajun AU - Yang , Lei AU - Xing , Xiaoqing AU - Zhong , Liuqiang JO - Journal of Computational Mathematics VL - 3 SP - 673 EP - 689 PY - 2024 DA - 2024/11 SN - 43 DO - http://doi.org/10.4208/jcm.2305-m2023-0088 UR - https://global-sci.org/intro/article_detail/jcm/23554.html KW - Iterative two-grid method, Convergence, Strongly nonlinear elliptic problems. AB -

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.

Zhan , JiajunYang , LeiXing , Xiaoqing and Zhong , Liuqiang. (2024). An Iterative Two-Grid Method for Strongly Nonlinear Elliptic Boundary Value Problems. Journal of Computational Mathematics. 43 (3). 673-689. doi:10.4208/jcm.2305-m2023-0088
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard