Linearly implicit methods for Allen-Cahn equation

Murat Uzunca and Bülent Karasözen

Applied Mathematics and Computation, 2023, vol. 450, issue C

Abstract: It is well known that the Allen-Cahn equation satisfies a nonlinear stability property, i.e., the free-energy functional decreases in time. Linearly implicit integrators have been developed for energy-preserving methods for conservative systems with polynomial Hamiltonians, which are based on the concept of polarization. In this paper, we construct linearly implicit methods for gradient flows preserving the energy dissipation by polarizing the free-energy functional. Two-step linearly implicit methods are derived for the Allen-Cahn equation inheriting energy dissipation law. Numerical experiments for one-, two-, and three-dimensional Allen-Cahn equations demonstrate the energy dissipation and the accuracy of the linearly implicit methods.

Keywords: Allen-Cahn equation; Gradient systems; Energy dissipation; Linearly implicit methods (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:450:y:2023:i:c:s0096300323001534

DOI: 10.1016/j.amc.2023.127984

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