Numerical analysis of an evolutionary variational–hemivariational inequality with application in contact mechanics

Mikaël Barboteu; Krzysztof Bartosz; Weimin Han

doi:10.1016/j.cma.2017.02.003

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Numerical analysis of an evolutionary variational–hemivariational inequality with application in contact mechanics

Journal article

Peer reviewed

Numerical analysis of an evolutionary variational–hemivariational inequality with application in contact mechanics

Mikaël Barboteu, Krzysztof Bartosz and Weimin Han

Computer methods in applied mechanics and engineering, Vol.318, pp.882-897

05/01/2017

DOI: 10.1016/j.cma.2017.02.003

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http://ruj.uj.edu.pl/xmlui/handle/item/40286View

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Abstract

Variational–hemivariational inequalities are useful in applications in science and engineering. This paper is devoted to numerical analysis for an evolutionary variational–hemivariational inequality. We introduce a fully discrete scheme for the inequality, using a finite element approach for the spatial approximation and a backward finite difference to approximate the time derivative. We present a Céa type inequality which is the starting point for error estimation. Then we apply the results in the numerical solution of a problem arising in contact mechanics, and derive an optimal order error estimate when the linear elements are used. Finally, we report numerical simulation results on solving a model contact problem, and provide numerical evidence on the theoretically predicted optimal order error estimate. •First paper on numerical analysis of evolutionary variational–hemivariational inequality problems.•A Céa type inequality for fully discrete numerical solutions.•An optimal order error estimate for linear element solutions.•Numerical evidence on the theoretically predicted optimal order error estimate.

Contact mechanics

Error estimation

Evolutionary variational–hemivariational inequality

Finite element method

Details

Title: Subtitle: Numerical analysis of an evolutionary variational–hemivariational inequality with application in contact mechanics
Creators: Mikaël Barboteu - Université de Perpignan
Krzysztof Bartosz - Jagiellonian University
Weimin Han - University of Iowa
Resource Type: Journal article
Publication Details: Computer methods in applied mechanics and engineering, Vol.318, pp.882-897
DOI: 10.1016/j.cma.2017.02.003
ISSN: 0045-7825
eISSN: 1879-2138
Publisher: Elsevier B.V
Grant note: DEC-2012/06/A/ST1/00262 / National Science Center of Poland DMS-1521684 / NSF
Language: English
Date published: 05/01/2017
Academic Unit: Mathematics
Record Identifier: 9984241045802771

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