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Adaptive finite elements for a certain class of variational inequalities of second kind. (English) Zbl 1239.65042

Summary: We extend our studies on finite element Galerkin schemes for elliptic variational inequalities of first to the one of second kind. Especially we perform the corresponding a posteriori error analysis for a simple friction problem and a model flow of a Bingham fluid.

Collecting the experiences from these examples, we propose a framework for deriving a posteriori error estimates for a certain class of problems given in an abstract setting describing elliptic variational problems of second kind.

Numerical examples and tests confirm our theoretical results.

MSC:
65K15Numerical methods for variational inequalities and related problems
49J40Variational methods including variational inequalities
74M10Friction (solid mechanics)
49M25Discrete approximations in calculus of variations
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