A priori error analysis of virtual element method for contact problem

Wang, Fei; Reddy, B Daya

A priori error analysis of virtual element method for contact problem

Journal Article

2022-04-01

Journal Title

Fixed Point Theory and Algorithms for Sciences and Engineering

Link to Journal

https://fixedpointtheoryandapplications.springeropen.com/

Publisher

Springer International Publishing

Abstract

As an extension of the finite element method, the virtual element method (VEM) can handle very general polygonal meshes, making it very suitable for non-matching meshes. In (Wriggers et al. in Comput. Mech. 58:1039–1050, 2016), the lowest-order virtual element method was applied to solve the contact problem of two elastic bodies on non-matching meshes. The numerical experiments showed the robustness and accuracy of the virtual element scheme. In this paper, we establish a priori error estimate of the virtual element method for the contact problem and prove that the lowest-order VEM achieves linear convergence order, which is optimal.