A virtual element method for the Cahn-Hilliard problem in mixed form

The paper is concerned with the construction and convergence analysis of the simplest C0 virtual element method for the Cahn-Hilliard problem in mixed form. This virtual element method leads to a low requirement on regularity and a treatment of general polygonal elements, including non-convex and degenerate elements. Moreover, by introducing two elliptic operators, we prove the L2-error estimate for concentration ϕ in the semidiscrete scheme. Furthermore, numerical results of the full discrete scheme are presented.