Geodesic
Prox-regularization and solution of ill-posed elliptic variational inequalities
Applications of Mathematics, Tome 42 (1997) no. 2, pp. 111-145 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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

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