A Higher Order Nonconforming Virtual Element Method for the Cahn–Hilliard Equation

Abstract In this paper we develop a fully nonconforming virtual element method of arbitrary approximation order for the two dimensional Cahn–Hilliard equation. We carry out the error analysis for the semidiscrete (continuous-in-time) scheme and verify the theoretical convergence result via numerical experiments. We present a fully discrete scheme which uses a convex splitting Runge–Kutta method to discretize in the temporal variable alongside the virtual element spatial discretization.