Rothe method and numerical analysis for history-dependent hemivariational inequalities with applications to contact mechanics

被引：0
作者：
Stanisław Migórski
Shengda Zeng
机构：
[1] Chengdu University of Information Technology,College of Applied Mathematics
[2] Jagiellonian University in Krakow,Chair of Optimization and Control
[3] Jagiellonian University in Krakow,Faculty of Mathematics and Computer Science
来源：
Numerical Algorithms | 2019年 / 82卷
关键词：
Hemivariational inequality; Clarke subgradient; History-dependent operator; Rothe method; Finite element method; Error estimates; Viscoelastic material; Frictional contact; 35L15; 35L86; 35L87; 74Hxx; 74M10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, an abstract evolutionary hemivariational inequality with a history-dependent operator is studied. First, a result on its unique solvability and solution regularity is proved by applying the Rothe method. Next, we introduce a numerical scheme to solve the inequality and derive error estimates. We apply the results to a quasistatic frictional contact problem in which the material is modeled with a viscoelastic constitutive law, the contact is given in the form of multivalued normal compliance, and friction is described with a subgradient of a locally Lipschitz potential. Finally, for the contact problem, we provide the optimal error estimate.
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页码：423 / 450
页数：27
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