A Hybrid High-Order method for the convective Cahn–Hilliard problem in mixed form

Florent A Chave (1) , Daniele Di Pietro (1) , Fabien A Marche (1, 2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 LEMON - Littoral, Environment: MOdels and Numerics

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.

Mots clés: Hybrid High-Order; Cahn–Hilliard equation; phase separation; mixed formulation; polyhedral meshes; arbitrary order

Domaines: Analyse numérique [math.NA]; Mathématiques [math]

Florent A Chave, Daniele Di Pietro, Fabien A Marche. A Hybrid High-Order method for the convective Cahn–Hilliard problem in mixed form. 2017. ⟨hal-01477247v1⟩