Fractional Crank-Nicolson-Galerkin finite element methods for nonlinear time fractional parabolic problems with time delay
Numerical Analysis
2021-09-10 v1 Numerical Analysis
Abstract
A linearized numerical scheme is proposed to solve the nonlinear time fractional parabolic problems with time delay. The scheme is based on the standard Galerkin finite element method in the spatial direction, the fractional Crank-Nicolson method and extrapolation methods in the temporal direction. A novel discrete fractional Gr\"{o}nwall inequality is established. Thanks to the inequality, the error estimate of fully discrete scheme is obtained. Several numerical examples are provided to verify the effectiveness of the fully discrete numerical method.
Keywords
Cite
@article{arxiv.2109.03994,
title = {Fractional Crank-Nicolson-Galerkin finite element methods for nonlinear time fractional parabolic problems with time delay},
author = {Lili Li and Mianfu She and Yuanling Niu},
journal= {arXiv preprint arXiv:2109.03994},
year = {2021}
}