Rothe method and numerical analysis for history-dependent hemivariational inequalities with applications to contact mechanics
Analysis of PDEs
2019-01-29 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1901.09522,
title = {Rothe method and numerical analysis for history-dependent hemivariational inequalities with applications to contact mechanics},
author = {Stanislaw Migorski and Shengda Zeng},
journal= {arXiv preprint arXiv:1901.09522},
year = {2019}
}