2023/01/07 by Jiajun Zhan, Lei Yang, Zhan, Jiajun +5
Engineering · Computer Science · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods
paper · pdf · doi:10.48550/arxiv.2301.02875
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.