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

Florent 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: Cahn–Hilliard equation; Phase separation; Arbitrary order; Hybrid High-Order; Polyhedral meshes; Mixed formulation

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

Florent Chave, Daniele Di Pietro, Fabien A Marche. A Hybrid High-Order method for the convective Cahn–Hilliard problem in mixed form. Cancès Clément; Omnes Pascal. Finite Volumes for Complex Applications VIII, 200, Springer, pp.517-525, 2017, Springer Proceedings in Mathematics & Statistics, 978-3-319-57393-9. ⟨10.1007/978-3-319-57394-6_54⟩. ⟨hal-01477247v2⟩