A two-derivative time integrator for the Cahn-Hilliard equation - Theodosiou, Eleni; Bringedal, Carina; Schütz, Jochen (Mathematical modelling and analysis, 2024)
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.