TY - JOUR
T1 - Analysis of L1-Galerkin FEMs for Time-Fractional Nonlinear Parabolic Problems
AU - Dongfang Li, Hong-Lin Liao, Weiwei Sun, Jilu Wang & Jiwei Zhang
JO - Communications in Computational Physics
VL - 1
SP - 86
EP - 103
PY - 2018
DA - 2018/03
SN - 24
DO - http://doi.org/10.4208/cicp.OA-2017-0080
UR - https://global-sci.org/intro/article_detail/cicp/10929.html
KW - Time-fractional nonlinear parabolic problems, L1-Galerkin FEMs, Error estimates, discrete fractional Gronwall type inequality, Linearized schemes.
AB - <p style="text-align: justify;">This paper is concerned with numerical solutions of time-fractional nonlinear
parabolic problems by a class of L1-Galerkin finite element methods. The analysis
of L1 methods for time-fractional nonlinear problems is limited mainly due to the lack
of a fundamental Gronwall type inequality. In this paper, we establish such a fundamental
inequality for the L1 approximation to the Caputo fractional derivative. In
terms of the Gronwall type inequality, we provide optimal error estimates of several
fully discrete linearized Galerkin finite element methods for nonlinear problems. The
theoretical results are illustrated by applying our proposed methods to the time fractional
nonlinear Huxley equation and time fractional Fisher equation.</p>