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arXiv · 1509.07384

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

Florent Chave·Daniele A. Di Pietro·Fabien Marche·Franck Pigeonneau
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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.

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Florent Chave, Daniele A. Di Pietro, Fabien Marche, Franck Pigeonneau. 2015-09-24. A Hybrid High-Order method for the Cahn-Hilliard problem in mixed form. https://doi.org/10.1137/15m1041055

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