Projection/fixed point method for solving a semilinear obstacle problem. (English) Zbl 1480.65156
Summary: 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 \(\mu\) of a convex continuous function. The function \(\mu\) 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.
MSC:
| 65K15 | Numerical methods for variational inequalities and related problems |
| 49J40 | Variational inequalities |
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