Prox-regularization and solution of ill-posed elliptic variational inequalities |
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Authors: | Alexander Kaplan Rainer Tichatschke |
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Affiliation: | (1) Dept. of Mathematics, Technical University of Darmstadt, D-64289 Darmstadt;(2) Dept. of Mathematics, University of Trier, D-54286 Trier, Germany |
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Abstract: | In this paper new methods for solving elliptic variational inequalities with weakly coercive operators are considered. The use of the iterative prox-regularization coupled with a successive discretization of the variational inequality by means of a finite element method ensures well-posedness of the auxiliary problems and strong convergence of their approximate solutions to a solution of the original problem.In particular, regularization on the kernel of the differential operator and regularization with respect to a weak norm of the space are studied. These approaches are illustrated by two nonlinear problems in elasticity theory. |
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Keywords: | prox-regularization ill-posed elliptic variational inequalities finite element methods two-body contact problem stable numerical methods |
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