Time-dependent variational inequalities for viscoelastic contact problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:136

Article

Han, WM ; Sofonea, M

关键词: variational inequality;    viscoelastic material;    contact;    normal compliance;    friction;    finite-element method;    semi-discrete scheme;    fully discrete scheme;    error estimates;   

DOI  :  10.1016/S0377-0427(00)00627-0

来源: Elsevier

【 摘 要 】

We consider a class of abstract evolutionary variational inequalities arising in the study of contact problems for viscoelastic materials. We prove an existence and uniqueness result, using standard arguments of time-dependent elliptic variational inequalities and Banach's fixed point theorem. We then consider numerical approximations of the problem. We use the finite element method to discretize the spatial domain and we introduce spatially semi-discrete and fully discrete schemes. For both schemes, we show the existence of a unique solution, and derive error estimates. Finally, we apply the abstract results to the analysis and numerical approximations of a viscoelastic contact problem with normal compliance and friction. (C) 2001 Elsevier Science B.V. All rights reserved.

【 授权许可】

Free