Finite element method for a stationary Stokes hemivariational inequality with slip boundary condition

Changjie Fang; Kenneth Czuprynski; Weimin Han; Xiaoliang Cheng; Xiaoxia Dai

doi:10.1093/imanum/drz032

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Finite element method for a stationary Stokes hemivariational inequality with slip boundary condition

Journal article

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Finite element method for a stationary Stokes hemivariational inequality with slip boundary condition

Changjie Fang, Kenneth Czuprynski, Weimin Han, Xiaoliang Cheng and Xiaoxia Dai

IMA journal of numerical analysis, Vol.40(4), pp.2696-2716

10/01/2020

DOI: 10.1093/imanum/drz032

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Abstract

This paper is devoted to the study of a hemivariational inequality problem for the stationary Stokes equations with a nonlinear slip boundary condition. The hemivariational inequality is formulated with the use of the generalized directional derivative and generalized gradient in the sense of Clarke. We provide an existence and uniqueness result for the hemivariational inequality. Then we apply the finite element method to solve the hemivariational inequality. The incompressibility constraint is treated through a mixed formulation. Error estimates are derived for numerical solutions. Numerical simulation results are reported to illustrate the theoretically predicted convergence orders.

Mathematics

Mathematics, Applied

Physical Sciences

Science & Technology

Details

Title: Subtitle: Finite element method for a stationary Stokes hemivariational inequality with slip boundary condition
Creators: Changjie Fang - Chongqing University of Posts and Telecommunications
Kenneth Czuprynski - University of Iowa
Weimin Han - University of Iowa
Xiaoliang Cheng - Zhejiang University
Xiaoxia Dai - Zhejiang University
Resource Type: Journal article
Publication Details: IMA journal of numerical analysis, Vol.40(4), pp.2696-2716
Publisher: OXFORD UNIV PRESS
DOI: 10.1093/imanum/drz032
ISSN: 0272-4979
eISSN: 1464-3642
Number of pages: 21
Grant note: DMS-1521684 / NSF; National Science Foundation (NSF) cstc2016jcyjA0163; cstc2018jcyjAX0605 / Basic and Advanced Research Project of CQ CSTC 823731 / European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant; SKA South Africa 11571311; 11771350 / National Natural Science Foundation of China; National Natural Science Foundation of China (NSFC)
Language: English
Date published: 10/01/2020
Academic Unit: Mathematics
Record Identifier: 9984241041802771

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