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Numerical Methods for Evolution Hemivariational Inequalities

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Advances in Variational and Hemivariational Inequalities

Part of the book series: Advances in Mechanics and Mathematics ((AMMA,volume 33))

Abstract

We consider numerical methods of solving evolution subdifferential inclusions of nonmonotone type. In the main part of the chapter we apply Rothe method for a class of second order problems. The method consists in constructing a sequence of piecewise constant and piecewise linear functions being a solution of approximate problem. Our main result provides a weak convergence of a subsequence to a solution of exact problem. Under some more restrictive assumptions we obtain also uniqueness of exact solution and a strong convergence result. Next, for the reference class of problems we apply a semi discrete Faedo-Galerkin method as well as a fully discrete one. For both methods we present a result on optimal error estimate.

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Acknowledgements

This research was supported by the Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme under Grant Agreement No. 295118, the International Project co-financed by the Ministry of Science and Higher Education of Republic of Poland under grant no. W111/7.PR/2012, the National Science Center of Poland under Maestro Advanced Project no. DEC-2012/06/A/ST1/00262, and the project Polonium “Mathematical and Numerical Analysis for Contact Problems with Friction” 2014/15 between the Jagiellonian University in Krakow and Université de Perpignan Via Domitia and the National Science Center of Poland under Grant no. N N201 604640.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30348, Krakow, Poland

    Krzysztof Bartosz

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  1. Krzysztof Bartosz
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Correspondence to Krzysztof Bartosz .

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Editors and Affiliations

  1. University of Iowa, Iowa City, IA, USA and Xi'an Jiaotong Universiry, Xi'an, China

    Weimin Han

  2. Faculty of Mathematics and Computer Scie Institute of Computer Science, Jagiellonian University, Kraków, Poland

    Stanisław Migórski

  3. Laboratoire de Mathématiques et Physique (LAMPS), Université de Perpignan Via Domitia, Perpignan, France

    Mircea Sofonea

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Bartosz, K. (2015). Numerical Methods for Evolution Hemivariational Inequalities. In: Han, W., Migórski, S., Sofonea, M. (eds) Advances in Variational and Hemivariational Inequalities. Advances in Mechanics and Mathematics, vol 33. Springer, Cham. https://doi.org/10.1007/978-3-319-14490-0_5

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