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High Order Finite Element Calculations for the Cahn-Hilliard Equation

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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 avoiding difficult computations or strategies like \(\mathcal{C}^{1}\) elements, adaptive mesh refinement, multi-grid resolution or isogeometric analysis. Beyond the classical benchmarks and comparisons with other existing methods, a numerical study has been carried out to investigate the influence of a polynomial approximation of the logarithmic free energy.

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Authors and Affiliations

  1. IRMAR, ENS Cachan Bretagne, CNRS, UEB, 35170, Bruz, France

    Ludovic Goudenège & Grégory Vial

  2. IRMAR, Université de Rennes 1, Campus de Beaulieu, 35000, Rennes, France

    Daniel Martin

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  1. Ludovic Goudenège
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  2. Daniel Martin
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  3. Grégory Vial
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Correspondence to Ludovic Goudenège.

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Goudenège, L., Martin, D. & Vial, G. High Order Finite Element Calculations for the Cahn-Hilliard Equation. J Sci Comput 52, 294–321 (2012). https://doi.org/10.1007/s10915-011-9546-7

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  • DOI: https://doi.org/10.1007/s10915-011-9546-7

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