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

Abstract

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.

22 pages, 6 figures, SIAM Journal on Numerical Analysis, 2016

References in corpus (1)

• A Hybrid High-Order method for the incompressible Navier--Stokes equations based on Temam's device

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• A Stable FE Method For the Space-Time Solution of the Cahn-Hilliard Equation
• Iterative solution to the biharmonic equation in mixed form discretized by the Hybrid High-Order method
• Weighted implicit-explicit discontinuous Galerkin methods for two-dimensional Ginzburg-Landau equations on general meshes