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

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

2010-03-04

arxiv.org/abs/1003.1077v1

Mathematics

Analysis of PDEs

Scientific paper

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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