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Domain Decomposition Methods for Problems of Unilateral Contact Between Elastic Bodies with Nonlinear Winkler Covers

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Domain Decomposition Methods in Science and Engineering XXI

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 98))

Abstract

In this paper we propose on continuous level a class of domain decomposition methods of Robin–Robin type to solve the problems of unilateral contact between elastic bodies with nonlinear Winkler covers. These methods are based on abstract nonstationary iterative algorithms for nonlinear variational equations in reflexive Banach spaces. We also provide numerical investigations of obtained methods using finite element approximations.

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Acknowledgements

This work was partially supported by Grant 23-08-12 of National Academy of Sciences of Ukraine.

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Authors and Affiliations

  1. Pidstryhach IAPMM NASU, Naukova 3-b, Lviv, 79000, Ukraine

    Ihor I. Prokopyshyn & Rostyslav M. Martynyak

  2. Ivan Franko National University of Lviv, Universytetska 1, Lviv, 79000, Ukraine

    Ivan I. Dyyak & Ivan A. Prokopyshyn

Authors
  1. Ihor I. Prokopyshyn
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  2. Ivan I. Dyyak
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  3. Rostyslav M. Martynyak
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  4. Ivan A. Prokopyshyn
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Corresponding author

Correspondence to Ihor I. Prokopyshyn .

Editor information

Editors and Affiliations

  1. INRIA, Rennes, France

    Jocelyne Erhel

  2. Section de Mathématiques, Université de Genève, Genève, Switzerland

    Martin J. Gander

  3. Laboratoire Analyse, Géometrie & Applications, Université Paris XIII, Villetaneuse, France

    Laurence Halpern

  4. INRIA, Rennes, France

    GĂ©raldine Pichot

  5. Laboratoire LMNO, Université de Caen, Caen, France

    Taoufik Sassi

  6. New York University Courant Institute, New York, New York, USA

    Olof Widlund

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Prokopyshyn, I.I., Dyyak, I.I., Martynyak, R.M., Prokopyshyn, I.A. (2014). Domain Decomposition Methods for Problems of Unilateral Contact Between Elastic Bodies with Nonlinear Winkler Covers. In: Erhel, J., Gander, M., Halpern, L., Pichot, G., Sassi, T., Widlund, O. (eds) Domain Decomposition Methods in Science and Engineering XXI. Lecture Notes in Computational Science and Engineering, vol 98. Springer, Cham. https://doi.org/10.1007/978-3-319-05789-7_71

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