MAXIMUM NORM CONVERGENCE OF NEWTON-MULTIGRID METHODS FOR ELLIPTIC QUASI-VARIATIONAL INEQUALITIES WITH NONLINEAR SOURCE TERMS

Abstract

In this paper, Newton-multigrid scheme on adaptive finite element discretisation is employed for solving elliptic quasi-variational inequalities with nonlinear source terms. We use Newton’s method as the outer iteration for the standard linearization, and using standard multigrid as the inner iteration for the solution of the Jacobian system at each step. The uniform convergence of Newton-multigrid methods is shown in the sense that the multigrid methods have a contraction number with respect to the maximum norm.