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 - <p style="text-align: justify;">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.</p>