Numerical approximation of an electro-elastic frictional contact problem modeled by hemivariational inequality

被引：2

作者：

Xu, Wei ^{[1
,2
]}

Huang, Ziping ^{[1
,2
]}

Han, Weimin ^{[3
]}

Chen, Wenbin ^{[4
,5
]}

Wang, Cheng ^{[1
]}

机构：

[1] Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China

[2] Tongji Zhejiang Coll, Jiaxing 314051, Peoples R China

[3] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

[4] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[5] Fudan Univ, Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2020年 / 39卷 / 04期

基金：

美国国家科学基金会;

关键词：

Hemivariational inequality; Galerkin approximation; Optimal order error estimate; Electro-elastic material; Frictional contact; UNILATERAL CONTACT;

D O I：

10.1007/s40314-020-01305-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, an electro-elastic frictional contact problem is studied numerically as a hemivariational inequality. Convergence of the Galerkin approximation for the hemivariational inequality is proved, and Cea's type inequalities are derived for error estimation. The results are applied to the electro-elastic contact problem, and an optimal order error estimate is deduced for linear element approximation. Finally, two numerical examples are reported, providing numerical evidence of the optimal convergence order theoretically predicted.

引用

页数：23

共 29 条

[1]

Atkinson K., 2009, Theoretical Numerical Analysis

[2] Numerical analysis of a dynamic piezoelectric contact problem arising in viscoelasticity [J].

Barboteu, M. ;

Fernandez, J. R. ;

Tarraf, R. .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2008, 197 (45-48) :3724-3732

[3] Numerical analysis of two frictionless elastic-piezoelectric contact problems [J].

Barboteu, M. ;

Fernandez, J. R. ;

Ouafik, Y. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 339 (02) :905-917

[4] Numerical analysis of a frictionless viscoelastic piezoelectric contact problem [J].

Barboteu, Mikael ;

Ramon Fernandez, Jose ;

Ouafik, Youssef .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2008, 42 (04) :667-682

[5] NUMERICAL ANALYSIS OF A HYPERBOLIC HEMIVARIATIONAL INEQUALITY ARISING IN DYNAMIC CONTACT [J].

Barboteu, Mikael ;

Bartosz, Krzysztof ;

Han, Weimin ;

Janiczko, Tomasz .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2015, 53 (01) :527-550

[6] Modeling and analysis of the unilateral contact of a piezoelectric body with a conductive support [J].

Barboteu, Mikael ;

Sofonea, Mircea .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 358 (01) :110-124

[7] SAINT-VENANTS PRINCIPLE IN LINEAR PIEZOELECTRICITY [J].

BATRA, RC ;

YANG, JS .

JOURNAL OF ELASTICITY, 1995, 38 (02) :209-218

[8]

Ciarlet P. G., 2002, Stud. Math. Appl.

[9]

Clarke F.H., 1983, OPTIMIZATION NONSMOO

[10]

Denkowski Z., 2003, An Introduction to Non-linear Analysis: Theory

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