Monotone multigrid methods based on element agglomeration coarsening away from the contact boundary for the Signorini's problem

Two multilevel schemes for solving inequality constrained finite element second-order elliptic problems, such as the Signorini's contact problem, are proposed and studied. The main ingredients of the schemes are that first they utilize element agglomeration coarsening away from the constraint set (boundary), which allows for easy construction of coarse level approximations that straightforwardly satisfy the fine-grid constraints. Second important feature of the schemes is that they provide monotone reduction of the energy functional throughout the multilevel cycles. This is achieved by using monotone smoothers (such as the projected Gauss–Seidel method) and due to the fact that the recursive application of the two-grid schemes is also monotone. The performance of the resulting methods is illustrated by numerical experiments on a model 2D Signorini's problem. Copyright 2004 © John Wiley & Sons, Ltd.