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

In: Optimization in Science and Engineering

Author

Listed:
  • Nina Ovcharova

    (Institute of Mathematics, Universität der Bundeswehr München, Department of Aerospace Engineering)

  • Joachim Gwinner

    (Institute of Mathematics, Universität der Bundeswehr München, Department of Aerospace 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.

Suggested Citation

  • Nina Ovcharova & Joachim Gwinner, 2014. "On the Discretization of Pseudomonotone Variational Inequalities with an Application to the Numerical Solution of the Nonmonotone Delamination Problem," Springer Books, in: Themistocles M. Rassias & Christodoulos A. Floudas & Sergiy Butenko (ed.), Optimization in Science and Engineering, edition 127, pages 393-405, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-0808-0_20
    DOI: 10.1007/978-1-4939-0808-0_20
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