• 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.