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Numerical analysis of an evolutionary variational–hemivariational inequality with application in contact mechanics.pdf
Available online at
ScienceDirect
Comput. Methods Appl. Mech. Engrg. 318 (2017) 882–897
/locate/cma
Numerical analysis of an evolutionary variational–hemivariational inequality with application in contact mechanics?
Mika?l Barboteua, Krzysztof Bartoszb, Weimin Hanc,?
a LAboratoire de Mathématiques et PhySique (LAMPS), Université de Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan, France b Faculty of Mathematics and Computer Science, Institute of Computer Science, Jagiellonian University, ul. ?ojasiewicza 6, 30348 Krakow,
Poland c Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
Received 6 December 2016; accepted 1 February 2017 Available online 16 February 2017
Highlights
? 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.
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. ?c 2017 Elsevier B.V. All rights reserved.
Keywords: Evolutionary variational–hemivariational inequality; Finite element method; Error estimation; Contact
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