An Iterative Two-Grid Method for Strongly Nonlinear Elliptic Boundary Value Problems (Journal of Computational Mathematics, 2024)
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 proposean iterative two-grid algorithm, in which a nonlinear problem is first solved on the coarsespace, and then a symmetric positive definite problem is solved on the fine space. Themain contribution in this paper is to establish a first convergence analysis, which requiresdealing with four coupled error estimates, for the iterative two-grid methods. We alsopresent some numerical experiments to confirm the efficiency of the proposed algorithm.
Keywords: Iterative two-grid method; Convergence; Strongly nonlinear elliptic problems.