Fast time-stepping discontinuous Galerkin method for the subdiffusion equation

09/06/2023

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by   Hui Zhang, et al.

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The nonlocality of the fractional operator causes numerical difficulties for long time computation of the time-fractional evolution equations. This paper develops a high-order fast time-stepping discontinuous Galerkin finite element method for the time-fractional diffusion equations, which saves storage and computational time. The optimal error estimate O(N^-p-1 + h^m+1 + ε N^rα) of the current time-stepping discontinuous Galerkin method is rigorous proved, where N denotes the number of time intervals, p is the degree of polynomial approximation on each time subinterval, h is the maximum space step, r≥1, m is the order of finite element space, and ε>0 can be arbitrarily small. Numerical simulations verify the theoretical analysis.