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Residual a Posteriori Error Estimation for Frictional Contact with Nitsche Method

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Abstract

We consider frictional contact problems in small strain elasticity discretized with finite elements and Nitsche method. Both bilateral and unilateral contact problems are taken into account, as well as both Tresca and Coulomb friction models. We derive residual a posteriori error estimates for each friction model, following (Chouly et al., in IMA J Numer Anal 38: 921–954, 2018). For the incomplete variant of Nitsche, we prove an upper bound for the dual norm of the residual, for Tresca and Coulomb friction, without any extra regularity and without a saturation assumption. We prove also local lower bounds. Numerical experiments allow to assess the accuracy of the estimates and their interest for adaptive meshing in different situations.

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Acknowledgements

The authors thank to the two anonymous referees for their comments that helped to improve the presentation of the results. R.A. was partially supported by ANID-Chile through the projects: Centro de Modelamiento Matemático (FB210005) of the PIA Program: Concurso Apoyo a Centros Científicos y Tecnológicos de Excelencia con Financiamiento Basal, and Fondecyt Regular No 1211649 F.C. work was partially supported by the I-Site BFC project NAANoD and the EIPHI Graduate School (contract ANR-17-EURE-0002). F.C. is grateful of the Center for Mathematical Modeling Grant FB20005.

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  1. Institut de Mathématiques de Bourgogne, Université de Bourgogne, 21078, Dijon, France

    Franz Chouly

  2. Departamento de Ingeniería Matemática and CI²MA, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    Rodolfo Araya & Franz Chouly

  3. Center for Mathematical Modeling and Department of Mathematical Engineering, IRL 2807 - CNRS, University of Chile, Santiago, Chile

    Franz Chouly

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  1. Rodolfo Araya
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Araya, R., Chouly, F. Residual a Posteriori Error Estimation for Frictional Contact with Nitsche Method. J Sci Comput 96, 87 (2023). https://doi.org/10.1007/s10915-023-02300-8

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