Alexander Kaplan, Dept. of Mathematics, Technical University of Darmstadt, D-64289 Darmstadt; Rainer Tichatschke, Dept. of Mathematics, University of Trier, D-54286 Trier, Germany
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.
Keywords: prox-regularization, ill-posed elliptic variational inequalities, finite element methods, two-body contact problem, stable numerical methods
Classification (MSC 1991): 35J85, 49A29, 49D45, 65K10, 73C30
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