The virtual element method for an obstacle problem of a Kirchhoff-Love plate

Abstract This paper is devoted to the numerical solution of a fourth-order elliptic variational inequality of the first kind by the virtual element method (VEM). The variational inequality models an obstacle problem for the Kirchhoff-Love plate. Both conforming and fully nonconforming VEMs are studied to solve the fourth-order elliptic variational inequality. Optimal order error estimates are derived in the discrete energy norm, under certain solution regularity assumptions. The primal-dual active algorithm is applied to solve the discrete problems. Numerical examples are reported to show the performance of the numerical methods and to illustrate the convergence orders of the numerical solutions.