Rothe method and numerical analysis for history-dependent hemivariational inequalities with applications to contact mechanics
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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.
KeywordsHemivariational inequality Clarke subgradient History-dependent operator Rothe method Finite element method Error estimates Viscoelastic material Frictional contact
Mathematics Subject Classification (2010)35L15 35L86 35L87 74Hxx 74M10
This project was supported by the H2020-MSCA-RISE-2018 Research and Innovation Staff Exchange Scheme Fellowship within the Project No. 823731 CONMECH, the National Science Center of Poland under Maestro Project No. UMO-2012/06/A/ST1/00262, and National Science Center of Poland under Preludium Project No. 2017/25/N/ST1/00611. It is also supported by the International Project co-financed by the Ministry of Science and Higher Education of Republic of Poland under Grant No. 3792/GGPJ/H2020/2017/0, Natural Sciences Foundation of Guangxi Grant No. 2018JJA110006, Beibu Gulf University Project No. 2018KYQD06, National Natural Science Foundation of China (Grant Nos. 11561007).
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