Multigrid Algorithms for Variational Inequalities

Abstract

We present an iterative scheme for obstacle problems described by variational inequalities. At each step of the iteration the method leads to a reduced linear (resp. nonlinear) algebraic system which is solved by a multigrid algorithm. Numerical results are given for the elastic-plastic torsion problem, the minimal surface over an obstacle and a stochastic inventory problem with impulse control. Key words. multigrid methods, variational and quasi-variational inequalities, obstacle problems, complementarily problems