A Nonconforming Virtual Element Method for a Fourth-order Hemivariational Inequality in Kirchhoff Plate Problem

Abstract

This paper is devoted to a fourth-order hemivariational inequality for a Kirchhoff plate problem. A solution existence and uniqueness result is proved for the hemivariational inequality through the analysis of a corresponding minimization problem. A nonconforming virtual element method is developed to solve the hemivariational inequality. An optimal order error estimate in a broken H2-norm is derived for the virtual element solutions under appropriate solution regularity assumptions. The discrete problem can be formulated as an optimization problem for a difference of two convex (DC) functions and a convergent algorithm is used to solve it. Computer simulation results on a numerical example are reported, providing numerical convergence orders that match the theoretical prediction.