A posteriori error estimates via equilibrated stress reconstructions for contact problems approximated by Nitsche's method
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 sh...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
24.09.2021
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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DOI: | 10.48550/arxiv.2109.11944 |