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Mesh and model adaptivity for frictional contact problems

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Abstract

The article focuses on adaptive finite element methods for frictional contact problems. The approach is based on a reformulation of the mixed form of the underlying Signorini problem with friction as a nonlinear variational equation using nonlinear complimentarity functions. The usual dual weighted residual framework for a posteriori error estimation is applied. However, we have to take into account the nonsmoothness of the problem formulation. Error identities for measuring the discretization as well as the model error with respect to a model hierarchy of friction laws are derived and a method for the numerical evaluation of them is proposed. The estimates are utilized in an adaptive framework, which balances the discretization and the model error. Several numerical examples substantiate the accuracy of the proposed estimates and the efficiency of the adaptive method.

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Acknowledgements

The author gratefully acknowledges the financial support by the German Research Foundation (DFG) within the subproject A5 of the transregional collaborative research centre (Transregio) 73 “Sheet-Bulk-Metal-Forming”.

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  1. Chair of Scientific Computing, Technische Universität Dortmund, Vogelpothsweg 87, 44227, Dortmund, Germany

    Andreas Rademacher

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Rademacher, A. Mesh and model adaptivity for frictional contact problems. Numer. Math. 142, 465–523 (2019). https://doi.org/10.1007/s00211-019-01044-8

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