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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.

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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