A priori and a posteriori error estimates for hp-FEM for a Bingham type variational inequality of the second kind

A hp-finite element discretization of a Bingham type variational inequality of the second kind is being analyzed. We prove convergence, including guaranteed convergence rates in the mesh size h and polynomial degree p of the discrete FE-solution. The friction functional may be regularized in which c...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2022-11, Vol.126, p.14-30
Main Authors: Banz, Lothar, Hernández, Orlando, Stephan, Ernst P.
Format: Article
Language:English
Subjects:
A posteriori error estimate
A priori error estimate
Bingham flow
hp-FEM
Variational inequalities of second kind
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Summary:A hp-finite element discretization of a Bingham type variational inequality of the second kind is being analyzed. We prove convergence, including guaranteed convergence rates in the mesh size h and polynomial degree p of the discrete FE-solution. The friction functional may be regularized in which case we also prove convergence and convergence rates in the regularization parameter ϵ. Moreover, we derive two families of reliable a posteriori error estimators which are applicable to any “approximation” of the exact solution and not only to the FE-solution and can therefore be coupled with an iterative solver. The exact computable member of each family of a posteriori error estimators with minimal value is proven to satisfy an efficiency estimate. Numerical results underline the theoretical finding.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2022.09.003