@Article{JCM-43-515,
author = {Quan , ChaoyuTang , Tao and Yang , Jiang},
title = {Numerical Energy Dissipation for Time-Fractional Phase-Field Equations},
journal = {Journal of Computational Mathematics},
year = {2024},
volume = {43},
number = {3},
pages = {515--539},
abstract = {<p style="text-align: justify;">The numerical integration of phase-field equations is a delicate task which needs to
recover at the discrete level intrinsic properties of the solution such as energy dissipation
and maximum principle. Although the theory of energy dissipation for classical phase field
models is well established, the corresponding theory for time-fractional phase-field models
is still incomplete. In this article, we study certain nonlocal-in-time energies using the
first-order stabilized semi-implicit L1 scheme. In particular, we will establish a discrete
fractional energy law and a discrete weighted energy law. The extension for a $(2−α)$-order
L1 scalar auxiliary variable scheme will be investigated. Moreover, we demonstrate that
the energy bound is preserved for the L1 schemes with nonuniform time steps. Several
numerical experiments are carried to verify our theoretical analysis.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2311-m2021-0199},
url = {http://global-sci.org/intro/article_detail/jcm/23548.html}
}