Monotone convergence of finite element approximations of obstacle problems

摘要

The purpose of the work is to study the monotone convergence of numerical solutions of obstacle problems under mesh refinement when the obstacle is convex. We prove monotone convergence of piecewise linear finite element approximations for one-dimensional obstacle problems. We demonstrate by giving a example that such monotone convergence will not hold in the two-dimensional case. (C) 2006 Elsevier Ltd. All rights reserved.