Geodesic
Prox-regularization and solution of ill-posed elliptic variational inequalities
Applications of Mathematics, Tome 42 (1997) no. 2, pp. 111-145.

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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.
DOI : 10.1023/A:1022243127667
Classification : 35J85, 35R25, 47H19, 49A29, 49D45, 49J40, 49M99, 65K10, 73C30
Keywords: prox-regularization; ill-posed elliptic variational inequalities; finite element methods; two-body contact problem; stable numerical methods; contact problem; strong convergence; weakly coercive operators 
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Kaplan, Alexander; Tichatschke, Rainer. Prox-regularization and solution of ill-posed elliptic variational inequalities. Applications of Mathematics, Tome 42 (1997) no. 2, pp. 111-145. doi : 10.1023/A:1022243127667. http://geodesic.mathdoc.fr/articles/10.1023/A:1022243127667/

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