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Media type:
E-Article
Title:
Conforming and nonconforming virtual element methods for a Kirchhoff plate contact problem
Contributor:
Wang, Fei;
Zhao, Jikun
Published:
Oxford University Press (OUP), 2021
Published in:
IMA Journal of Numerical Analysis, 41 (2021) 2, Seite 1496-1521
Language:
English
DOI:
10.1093/imanum/draa005
ISSN:
0272-4979;
1464-3642
Origination:
Footnote:
Description:
AbstractWe establish a general framework to study the conforming and nonconforming virtual element methods (VEMs) for solving a Kirchhoff plate contact problem with friction, which is a fourth-order elliptic variational inequality (VI) of the second kind. This VI contains a non-differentiable term due to the frictional contact. This theoretical framework applies to the existing virtual elements such as the conforming element, the $C^0$-continuous nonconforming element and the fully nonconforming Morley-type element. In the unified framework we derive a priori error estimates for these virtual elements and show that they achieve optimal convergence order for the lowest-order case. For demonstrating the performance of the VEMs we present some numerical results that confirm the theoretical prediction of the convergence order.