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Coupling regularization and adaptive hp-BEM for the solution of a delamination problem

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Abstract

In this paper, we couple regularization techniques with the adaptive hp-version of the boundary element method (hp-BEM) for the efficient numerical solution of linear elastic problems with nonmonotone contact boundary conditions. As a model example we treat the delamination of composite structures with a contaminated interface layer. This problem has a weak formulation in terms of a nonsmooth variational inequality. The resulting hemivariational inequality is first regularized and then discretized by an adaptive hp-BEM. We give conditions for the uniqueness of the solution and provide an a-priori error estimate. Furthermore, we prove the very first a-posteriori error estimate for the nonsmooth variational problem utilizing a novel mixed regularized formulation, thus enabling hp-adaptivity. Various numerical experiments illustrate the behavior, strengths and limitations of the proposed high-order approximation scheme.

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Acknowledgements

The authors are grateful to J. Gwinner for the helpful discussions and comments.

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Authors and Affiliations

  1. Universität der Bundeswehr München, 85577, Neubiberg/Munich, Germany

    Nina Ovcharova

  2. Department of Mathematics, University of Salzburg, Hellbrunner Straße 34, 5020, Salzburg, Austria

    Lothar Banz

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  1. Nina Ovcharova
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  2. Lothar Banz
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Correspondence to Nina Ovcharova.

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Ovcharova, N., Banz, L. Coupling regularization and adaptive hp-BEM for the solution of a delamination problem. Numer. Math. 137, 303–337 (2017). https://doi.org/10.1007/s00211-017-0879-5

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  • DOI: https://doi.org/10.1007/s00211-017-0879-5

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