Generalized Penalty Method for Elliptic Variational-Hemivariational Inequalities

被引:37
作者
Xiao, Yi-bin [1 ]
Sofonea, Mircea [2 ]
机构
[1] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China
[2] Univ Perpignan, Lab Math & Phys, Via Domitia,52 Ave Paul Alduy, F-66860 Perpignan, France
基金
中国国家自然科学基金; 欧盟地平线“2020”;
关键词
Variational-hemivariational inequality; Clarke subdifferential; Penalty method; Convergence; Frictional contact; NUMERICAL-ANALYSIS; WELL-POSEDNESS;
D O I
10.1007/s00245-019-09563-4
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider an elliptic variational-hemivariational inequality with constraints in a reflexive Banach space, denoted P, to which we associate a sequence of inequalities {P-n}. For each n is an element of N, P-n is a variational-hemivariational inequality without constraints, governed by a penalty parameter lambda(n) and an operator P-n. Such inequalities are more general than the penalty inequalities usually considered in literature which are constructed by using a fixed penalty operator associated to the set of constraints of P. We provide the unique solvability of inequality P-n. Then, under appropriate conditions on operators P-n, we state and prove the convergence of the solution of P-n to the solution of P. This convergence result extends the results previously obtained in the literature. Its generality allows us to apply it in various situations which we present as examples and particular cases. Finally, we consider a variational-hemivariational inequality with unilateral constraints which arises in Contact Mechanics. We illustrate the applicability of our abstract convergence result in the study of this inequality and provide the corresponding mechanical interpretations.
引用
收藏
页码:789 / 812
页数:24
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