Numerical analysis of history-dependent variational–hemivariational inequalities with applications in contact mechanics

Wei Xu; Ziping Huang; Weimin Han; Wenbin Chen; Cheng Wang

doi:10.1016/j.cam.2018.08.046

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Numerical analysis of history-dependent variational–hemivariational inequalities with applications in contact mechanics

Journal article

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Numerical analysis of history-dependent variational–hemivariational inequalities with applications in contact mechanics

Wei Xu, Ziping Huang, Weimin Han, Wenbin Chen and Cheng Wang

Journal of computational and applied mathematics, Vol.351, pp.364-377

05/01/2019

DOI: 10.1016/j.cam.2018.08.046

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Abstract

This paper is devoted to numerical analysis of history-dependent variational– hemivariational inequalities arising in contact problems for viscoelastic material. We introduce both temporally semi-discrete approximation and fully discrete approximation for the problem, where the temporal integration is approximated by a trapezoidal rule and the spatial variable is approximated by the finite element method. We analyze the discrete schemes and derive error bounds. The results are applied for the numerical solution of a quasistatic contact problem. For the linear finite element method, we prove that the error estimation for the numerical solution is of optimal order under appropriate solution regularity assumptions.

Clarke subdifferential

Contact mechanics

Finite element method

History-dependent operator

Optimal order error estimate

Variational–Hemivariational inequality

Details

Title: Subtitle: Numerical analysis of history-dependent variational–hemivariational inequalities with applications in contact mechanics
Creators: Wei Xu - Tongji University
Ziping Huang - Tongji University
Weimin Han - University of Iowa
Wenbin Chen - Fudan University
Cheng Wang - Tongji University
Resource Type: Journal article
Publication Details: Journal of computational and applied mathematics, Vol.351, pp.364-377
DOI: 10.1016/j.cam.2018.08.046
ISSN: 0377-0427
eISSN: 1879-1778
Publisher: Elsevier B.V
Grant note: DOI: 10.13039/100000001, name: National Science Foundation, award: DMS-1521684; DOI: 10.13039/501100001809, name: National Natural Science Foundation of China, award: 11331004, 11671098, 91630309; DOI: 10.13039/501100002338, name: Ministry of Education of the People's Republic of China; DOI: 10.13039/501100003512, name: State Administration of Foreign Experts Affairs, award: B08018
Language: English
Date published: 05/01/2019
Academic Unit: Mathematics
Record Identifier: 9984240876702771

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