A Hybrid High-Order Method for the Convective Cahn–Hilliard Problem in Mixed Form

Abstract

We propose a novel Hybrid High-Order method for the Cahn-Hilliard problem with convection. The proposed method is valid in two and three space dimensions, and it supports arbitrary approximation orders on general meshes containing polyhedral elements and nonmatching interfaces. An extensive numerical validation is presented, which shows robustness with respect to the Péclet number. Cahn-Hilliard equationLet Ω ⊂ R d , d ∈ {2, 3}, denote a bounded connected convex polyhedral domain with Lipschitz boundary ∂ Ω and outward normal n, and let t F > 0. The convective Cahn-Hilliard problem consists in finding the order-parameter c : Ω × (0,t F ] → R and the chemical potential w :