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arXiv · 1003.1077

High order finite element calculations for the deterministic Cahn-Hilliard equation

Ludovic Goudenège·Daniel Martin·Grégory Vial
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Abstract

In this work, we propose a numerical method based on high degree continuous nodal elements for the Cahn-Hilliard evolution. The use of the p-version of the finite element method proves to be very efficient and favorably compares with other existing strategies (C^1 elements, adaptive mesh refinement, multigrid resolution, etc). Beyond the classical benchmarks, a numerical study has been carried out to investigate the influence of a polynomial approximation of the logarithmic free energy and the bifurcations near the first eigenvalue of the Laplace operator.

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Ludovic Goudenège, Daniel Martin, Grégory Vial. 2010-03-04. High order finite element calculations for the deterministic Cahn-Hilliard equation. https://doi.org/10.1007/s10915-011-9546-7

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