LDG method with the fast time technique for the two-dimensional fractional mobile/immobile convection-diffusion model

In this paper a fast algorithm is presented for numerically solving a two-dimensional fractional mobile/immobile convection-diffusion model, where the second-order time scheme of the integer derivative and the F L2-1 formula of the time Caputo fractional derivative are used in the time direction, and the local discontinuous Galerkin (LDG) method is developed to approximate the space direction.The stability of the fully discrete LDG scheme is proven, and the a priori error result with O(t 2 + h k+1 + ) is derived, where is the tolerance error.Finally, some numerical results with Q k (k = 0, 1, 2) elements are given to verify our theoretical results.