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+hm+1+εNrα) 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.Comment: 21 pages, 1 figure,4 table