Nonconforming virtual element methods for the fourth-order variational inequalities of the first kind

Abstract

We study the C0 nonconforming and fully nonconforming virtual element methods (VEMs) for solving two Kirchhoff plate problems, which are fourth-order variational inequalities of the first kind. For the Kirchhoff plate obstacle problem, we propose a modified fully nonconforming virtual element method. A priori error estimations are established for both the C0 nonconforming and fully nonconforming VEMs for the two Kirchhoff plate problems, and we show that the lowest-order VEMs achieve optimal convergence order. Two numerical examples are presented to support the theoretical results.