Analysis of multilevel finite volume approximation of 2D convective Cahn–Hilliard equation

In this work, four finite volume methods have been constructed to solve the 2D convective Cahn–Hilliard equation with specified initial condition and periodic boundary conditions. We prove existence and uniqueness of solutions. The stability and convergence analysis of the numerical methods have been discussed thoroughly. The nonlinear terms are approximated by a linear expression based on Mickens’ rule (Mickens, Nonstandard finite difference models of differential equations. World Scientific, Singapore, 1994) of nonlocal approximations of nonlinear terms. Numerical experiments for a test problem have been carried out to test all methods.