TITLE:
ADI Finite Element Method for 2D Nonlinear Time Fractional Reaction-Subdiffusion Equation
AUTHORS:
Peng Zhu, Shenglan Xie
KEYWORDS:
Nonlinear Fractional Differential Equation, Alternating Direction Implicit Method, Finite Element Method, Riemann-Liouville Fractional Derivative
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.6 No.4,
December
21,
2016
ABSTRACT: In this paper, an alternating direction Galerkin finite element method is
presented for solving 2D time fractional reaction sub-diffusion equation with
nonlinear source term. Firstly, one order implicit-explicit method is used for
time discretization, then Galerkin finite element method is adopted for spatial
discretization and obtain a fully discrete linear system. Secondly, Galerkin
alternating direction procedure for the system is derived by adding an extra
term. Finally, the stability and convergence of the method are analyzed
rigorously. Numerical results confirm the accuracy and efficiency of the
proposed method.