Numerical Approximation of a Unilateral Obstacle Problem

Numerical Approximation of a Unilateral Obstacle Problem

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Article ID: iaor20122828
Volume: 153
Issue: 1
Start Page Number: 177
End Page Number: 194
Publication Date: Apr 2012
Journal: Journal of Optimization Theory and Applications
Authors: ,
Keywords: approximation
Abstract:

We consider a reformulation of the unilateral obstacle problem presented by the authors (Addou and Mermri in Math‐Rech. Appl. 2:59–69, 2000). This reformulation introduces a continuous function, whose subdifferential characterizes the noncontact domain. Our goal in this paper is to give a numerical approximation of the solution of the reformulated problem. We consider discretization of the problem based on finite element method. Then we prove the convergence of the approximate solution to the exact one. Some numerical tests on one‐dimensional obstacle problem are provided.

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