A Weak Galerkin Finite Element Method for High Dimensional Time-fractional Diffusion Equation.

• We have provided comparison of CPU time for the standard WG-FEM and the fast WG-FEM in Table 4. • All references have been updated. • We have explained the super-convergence phenomena of | | ∇ w (e h) | | in the numerical experiments. • We have re-phased the "a new application of WG-FEM" according to reviewer's sugguestion. • The definition of Pk (K) has been corrected. • All minor mistakes pointed out by the reviewers have been corrected accordingly. • A detailed response to reviewers is attached to the revised manuscript. This paper is concerned with the application of a weak Galerkin finite element method (WG-FEM) to the time-fractional diffusion equation. The WG-FEM with L1-formula and the fast evaluation scheme based on WG-FEM are designed. The optimal convergence rates for both semi-discrete and fully discrete WG-FEM schemes are obtained, and the stability analysis for the semi-discrete WG-FEM is derived. Numerical experiments are implemented to verify the theoretical results. [ABSTRACT FROM AUTHOR]