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Zbl 1239.65042
Hage, D.; Klein, N.; Suttmeier, F.T.
Adaptive finite elements for a certain class of variational inequalities of second kind. (English)
[J] Calcolo 48, No. 4, 293-305 (2011). ISSN 0008-0624; ISSN 1126-5434/e

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.\par 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.\par Numerical examples and tests confirm our theoretical results.

MSC 2000:: *65K15
49J40 Variational methods including variational inequalities
74M10 Friction
49M25 Finite difference methods

Keywords: Bingham fluid; friction problem; a posteriori error estimate; variational inequality; finite element method; adaptivity; Galerkin schemes; Numerical examples

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Zentralblatt MATH Berlin [Germany]