Projection/fixed point method for solving a semilinear obstacle problem

Abstract

In this paper, we present a reformulation of a unilateral semilinear obstacle problem as a projection/fixed point problem based on appropriate variational inequality of the second kind and the subdifferential μ of a convex continuous function. The function μ leads to the characterization of the contact domain. Then we present the algorithms to solve the reformulated problem. We approximate the continuous problem by finite element method, then we present the analysis of the discrete problem and prove the convergence of the approximate solutions to the exact one.

Keywords:

• Variational inequality
• obstacle problem
• semilinear
• numerical method
• approximation

2010 Mathematics Subject Classifications:

• 65K15
• 49J40

Acknowledgments

We thank two anonymous referees for carefully reading the first version of the paper and for their helpful comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).