Numerical analysis of history-dependent variational-hemivariational inequalities

Shufen Wang; Wei Xu; Weimin Han; Wenbin Chen

doi:10.1007/s11425-019-1672-4

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Numerical analysis of history-dependent variational-hemivariational inequalities

Journal article

Peer reviewed

Numerical analysis of history-dependent variational-hemivariational inequalities

Shufen Wang, Wei Xu, Weimin Han and Wenbin Chen

Science China. Mathematics, Vol.63(11), pp.2207-2232

11/01/2020

DOI: 10.1007/s11425-019-1672-4

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Abstract

In this paper, numerical analysis is carried out for a class of history-dependent variational-hemivariational inequalities by arising in contact problems. Three different numerical treatments for temporal discretization are proposed to approximate the continuous model. Fixed-point iteration algorithms are employed to implement the implicit scheme and the convergence is proved with a convergence rate independent of the time step-size and mesh grid-size. A special temporal discretization is introduced for the history-dependent operator, leading to numerical schemes for which the unique solvability and error bounds for the temporally discrete systems can be proved without any restriction on the time step-size. As for spatial approximation, the finite element method is applied and an optimal order error estimate for the linear element solutions is provided under appropriate regularity assumptions. Numerical examples are presented to illustrate the theoretical results.

Mathematics

Mathematics, Applied

Physical Sciences

Science & Technology

Details

Title: Subtitle: Numerical analysis of history-dependent variational-hemivariational inequalities
Creators: Shufen Wang - Fudan University
Wei Xu - Faculty of Science, Tongji Zhejiang College, Jiaxing, China
Weimin Han - University of Iowa
Wenbin Chen - Fudan University
Resource Type: Journal article
Publication Details: Science China. Mathematics, Vol.63(11), pp.2207-2232
DOI: 10.1007/s11425-019-1672-4
ISSN: 1674-7283
eISSN: 1869-1862
Publisher: SCIENCE PRESS
Number of pages: 26
Grant note: 11671098; 91630309 / National Natural Science Foundation of China; National Natural Science Foundation of China (NSFC) Institute of Scientific Computation and Financial Data Analysis, Shanghai University of Finance and Economics B08018 / Higher Education Discipline Innovation Project (111 Project)
Language: English
Date published: 11/01/2020
Academic Unit: Mathematics
Record Identifier: 9984241151102771

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