Overlapping Domain Decomposition Method for a Noncoercive System of Quasi-Variational Inequalities Related to the Hamilton–Jacobi–Bellman Equation

Abstract

This paper deals with numerical analysis of an overlapping Schwarz method on nonmatching grids for a noncoercive system of quasi-variational inequalities related to the Hamilton–Jacobi–Bellman equation. We prove that the discrete alternating Schwarz sequences on every subdomain converge monotonically into the unique solution of the discrete problem and geometrically in uniform norm. Optimally L^∞-error estimates are also established.