Energy Stable L2 Schemes for Time-Fractional Phase-Field Equations
Numerical Analysis
2022-04-13 v1 Numerical Analysis
Abstract
In this article, the energy stability of two high-order L2 schemes for time-fractional phase-field equations is established. We propose a reformulation of the L2 operator and also some new properties on it. We prove the energy boundedness (by initial energy) of an L2 scalar auxiliary variable scheme for any phase-field equation and the fractional energy law of an implicit-explicit L2 Adams--Bashforth scheme for the Allen--Cahn equation. The stability analysis is based on a new Cholesky decomposition proposed recently by some of us.
Keywords
Cite
@article{arxiv.2108.08437,
title = {Energy Stable L2 Schemes for Time-Fractional Phase-Field Equations},
author = {Chaoyu Quan and Boyi Wang},
journal= {arXiv preprint arXiv:2108.08437},
year = {2022}
}