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On the Discretization of Pseudomonotone Variational Inequalities with an Application to the Numerical Solution of the Nonmonotone Delamination Problem

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Optimization in Science and Engineering

Abstract

In this paper we present an approximation procedure for pseudomonotone variational inequalities in general reflexive Banach spaces. Under an appropriate coerciveness condition we obtain a convergence result for this method. Then we show that hemivariational inequalities in linear elasticity are pseudomonotone. Thus our approximation method can be applied to nonmonotone contact. Here we give an application to a delamination problem in 2D. We sketch how regularization of nonsmooth functionals together with finite element approximation lead to an efficient numerical solution method for these problems.

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Author information

Authors and Affiliations

  1. Department of Aerospace Engineering, Institute of Mathematics, Universität der Bundeswehr München, Munich, Germany

    Nina Ovcharova & Joachim Gwinner

Authors
  1. Nina Ovcharova
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  2. Joachim Gwinner
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Corresponding author

Correspondence to Nina Ovcharova .

Editor information

Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Princeton University Dept. Chemical Engineering, Princeton, New Jersey, USA

    Christodoulos A. Floudas

  3. Dept. Industrial & Systems Engineering, Texas A&M University, College Station, Texas, USA

    Sergiy Butenko

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Ovcharova, N., Gwinner, J. (2014). On the Discretization of Pseudomonotone Variational Inequalities with an Application to the Numerical Solution of the Nonmonotone Delamination Problem. In: Rassias, T., Floudas, C., Butenko, S. (eds) Optimization in Science and Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0808-0_20

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