@Article{NMTMA-15-4,
author = {Liao, Hong-Lin and Wang, Jindi and Zhu, Xiaohan and Wang, Jindi},
title = {The Variable-Step L1 Scheme Preserving a Compatible Energy Law for Time-Fractional Allen-Cahn Equation},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2022},
volume = {15},
number = {4},
pages = {1128--1146},
abstract = {<p style="text-align: justify;">In this work, we revisit the adaptive L1 time-stepping scheme for solving the time-fractional Allen-Cahn equation in the Caputo’s form. The L1 implicit
scheme is shown to preserve a variational energy dissipation law on arbitrary nonuniform time meshes by using the recent discrete analysis tools, i.e., the discrete orthogonal convolution kernels and discrete complementary convolution kernels. Then the
discrete embedding techniques and the fractional Grönwall inequality are applied
to establish an $L^2$ norm error estimate on nonuniform time meshes. An adaptive
time-stepping strategy according to the dynamical feature of the system is presented
to capture the multi-scale behaviors and to improve the computational performance.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2022-0011s},
url = {https://global-sci.com/article/90284/the-variable-step-l1-scheme-preserving-a-compatible-energy-law-for-time-fractional-allen-cahn-equation}
}