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ADI Finite Element Method for 2D Nonlinear Time Fractional Reaction-Subdiffusion Equation

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Document pages: 21 pages

Abstract: In this paper, an alternating direction Galerkin finite element method ispresented for solving 2D time fractional reaction sub-diffusion equation withnonlinear source term. Firstly, one order implicit-explicit method is used fortime discretization, then Galerkin finite element method is adopted for spatialdiscretization and obtain a fully discrete linear system. Secondly, Galerkinalternating direction procedure for the system is derived by adding an extraterm. Finally, the stability and convergence of the method are analyzedrigorously. Numerical results confirm the accuracy and efficiency of theproposed method.

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