In this paper we develop a fully nonconforming virtual element method (VEM) 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.

翻译：本文针对二维Cahn-Hilliard方程，提出了一种任意逼近阶的完全非协调虚拟元方法（VEM）。我们对半离散（时间连续）格式进行了误差分析，并通过数值实验验证了理论收敛结果。此外，我们提出了一种全离散格式，该格式在虚拟元空间离散的基础上，采用凸分裂Runge-Kutta方法对时间变量进行离散化。