Uniform Convergence of Multigrid Methods for Elliptic Quasi-Variational Inequalities and Its Implementation - Belouafi, Mohammed Essaid; Beggas, Mohammed; Nesba, Nour El Houda (Communications in Mathematics and Applications, 2023)
In this paper, algebraic multigrid methods on adaptive finite element discretisation are applied for solving elliptic quasi-variational inequalities. The uniform convergence of the multigrid scheme has been established which proves that the multigrid methods have a contraction number with respect to the maximum norm. Numerical results which demonstrate the high efficiency of these methods are given for a quasi-variational inequality arising from impulse control problem on a domain with nonpolygonal boundaries.
Keywords: Quasi-variational inequality; Finite element method; HJB equation; Multigrid method