Autor: |
Di Pietro, Daniele Antonio, Fontana, Ilaria, Kazymyrenko, Kyrylo |
Rok vydání: |
2021 |
Předmět: |
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Druh dokumentu: |
Working Paper |
Popis: |
We present an a posteriori error estimate based on equilibrated stress reconstructions for the finite element approximation of a unilateral contact problem with weak enforcement of the contact conditions. We start by proving a guaranteed upper bound for the dual norm of the residual. This norm is shown to control the natural energy norm up to a boundary term, which can be removed under a saturation assumption. The basic estimate is then refined to distinguish the different components of the error, and is used as a starting point to design an algorithm including adaptive stopping criteria for the nonlinear solver and automatic tuning of a regularization parameter. We then discuss an actual way of computing the stress reconstruction based on the Arnold-Falk-Winther finite elements. Finally, after briefly discussing the efficiency of our estimators, we showcase their performance on a panel of numerical tests. |
Databáze: |
arXiv |
Externí odkaz: |
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