Journal article
Numerical Analysis of a Dynamic Contact Problem with History-Dependent Operators
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, Vol.13(3), pp.569-594
08/01/2020
DOI: 10.4208/nmtma.OA-2019-0130
Abstract
In this paper, we study a dynamic contact model with long memory which allows both the convex potential and nonconvex superpotentials to depend on history-dependent operators. The deformable body consists of a viscoelastic material with long memory and the process is assumed to be dynamic. The contact involves a nonmonotone Clarke subdifferential boundary condition and the friction is modeled by a version of the Coulomb's law of dry friction with the friction bound depending on the total slip. We introduce and study a fully discrete scheme of the problem, and derive error estimates for numerical solutions. Under appropriate solution regularity assumptions, an optimal order error estimate is derived for the linear finite element method. This theoretical result is illustrated numerically.
Details
- Title: Subtitle
- Numerical Analysis of a Dynamic Contact Problem with History-Dependent Operators
- Creators
- Hailing Xuan - Zhejiang UniversityXiaoliang Cheng - Zhejiang UniversityWeimin Han - Univ Iowa, Dept Math, Iowa City, IA 52242 USAQichang Xiao - Zhejiang University
- Resource Type
- Journal article
- Publication Details
- NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, Vol.13(3), pp.569-594
- Publisher
- GLOBAL SCIENCE PRESS
- DOI
- 10.4208/nmtma.OA-2019-0130
- ISSN
- 1004-8979
- eISSN
- 2079-7338
- Number of pages
- 26
- Grant note
- 823731 / European Union; European Commission
- Language
- English
- Date published
- 08/01/2020
- Academic Unit
- Mathematics
- Record Identifier
- 9984241160302771
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