An iterative two-grid method for strongly nonlinear elliptic boundary value problems

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 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.