Numerical analysis of history-dependent variational-hemivariational inequalities with applications to contact problems

作者：Sofonea Mircea^*; Han Weimin; Migorski Stanislaw

来源：European Journal of Applied Mathematics, 2015, 26(04): 427-452.

DOI：10.1017/S095679251500011X

• Variational-hemivariational inequality
• Clarke subdifferential
• history-dependent operator
• Continuous dependence
• Finite element method
• Convergence
• Error estimates
• Viscoelastic material
• Frictional contact
• Weak solution

A new class of history-dependent variational-hemivariational inequalities was recently studied in Migorski et al. (2015 Nonlinear Anal. Ser. B: Real World Appl. 22, 604-618). There, an existence and uniqueness result was proved and used in the study of a mathematical model which describes the contact between a viscoelastic body and an obstacle. The aim of this paper is to continue the analysis of the inequalities introduced in Migoki et al. (2015 Nonlinear Anal. Ser. B: Real World Appl. 22, 604-618) and to provide their numerical analysis. We start with a continuous dependence result. Then we introduce numerical schemes to solve the inequalities and derive error estimates. We apply the results to a quasistatic frictional contact problem in which the material is modelled with a viscoelastic constitutive law, the contact is given in the form of normal compliance, and friction is described with a total slip-dependent version of Coulomb's law.

• 出版日期2015-8
• 单位西安交通大学