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A two-derivative time integrator for the Cahn-Hilliard equation

    Eleni Theodosiou Affiliation
    ; Carina Bringedal Affiliation
    ; Jochen Schütz Affiliation

Abstract

This paper presents a two-derivative energy-stable method for the Cahn-Hilliard equation. We use a fully implicit time discretization with the addition of two stabilization terms to maintain the energy stability. As far as we know, this is the first time an energy-stable multiderivative method has been developed for phase-field models. We present numerical results of the novel method to support our mathematical analysis. In addition, we perform numerical experiments of two multiderivative predictor-corrector methods of fourth and sixth-order accuracy, and we show numerically that all the methods are energy stable.

Keyword : multiderivative methods, high-order methods, Cahn-Hilliard equation, energy-stable methods

How to Cite
Theodosiou, E., Bringedal, C., & Schütz, J. (2024). A two-derivative time integrator for the Cahn-Hilliard equation. Mathematical Modelling and Analysis, 29(4), 714–730. https://doi.org/10.3846/mma.2024.20646
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Nov 22, 2024
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