A Hybrid High-Order Method for the Cahn-Hilliard problem in Mixed Form

In this work we develop a fully implicit Hybrid High-Order algorithm for the Cahn– 5 Hilliard problem in mixed form. The space discretization hinges on local reconstruction operators 6 from hybrid polynomial unknowns at elements and faces. The proposed method has several ad7 vantageous features: (i) It supports fairly general meshes possibly containing polyhedral elements 8 and nonmatching interfaces; (ii) it allows arbitrary approximation orders; (iii) it has a moderate 9 computational cost thanks to the possibility of locally eliminating element-based unknowns by static 10 condensation. We perform a detailed stability and convergence study, proving optimal convergence 11 rates in energy-like norms. Numerical validation is also provided using some of the most common 12 tests in the literature. 13 2010 Mathematics Subject Classification: 65N08, 65N30, 65N12 14