%0 Journal Article
%T A Hybrid High-Order method for the Cahn-Hilliard problem in mixed form
%A Florent Chave
%A Daniele A. Di Pietro
%A Fabien Marche
%A Franck Pigeonneau
%J Mathematics
%D 2015
%I arXiv
%X In this work, we develop a fully implicit Hybrid High-Order algorithm for the Cahn-Hilliard problem in mixed form. The space discretization hinges on local reconstruction operators from hybrid polynomial unknowns at elements and faces. The proposed method has several assets: (i) It supports fairly general meshes possibly containing polygonal elements and nonmatching interfaces; (ii) it allows arbitrary approximation orders; (iii) it has a moderate computational cost thanks to the possibility of locally eliminating element-based unknowns by static condensation. We perform a detailed stability and convergence study, proving optimal convergence rates in energy-like norms. Numerical validation is also provided using some of the most common tests in the literature.
%U http://arxiv.org/abs/1509.07384v1