Article
MSC:
35J85,
35R25,
47H19,
49A29,
49D45,
49J40,
49M99,
65K10,
73C30 | MR 1430405 | Zbl 0899.35040 | DOI: 10.1023/A:1022243127667
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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
prox-regularization; ill-posed elliptic variational inequalities; finite element methods; two-body contact problem; stable numerical methods; contact problem; strong convergence; weakly coercive operators
Summary:
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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