An alternating direction implicit Galerkin finite element method for the distributed-order time-fractional mobile-immobile equation in two dimensions

摘要

In this paper, we shall present the alternating direction implicit (ADI) Galerkin finite element method (FEM) for solving the distributed-order time-fractional mobile-immobile equation in two dimensions. In the time direction, the backward Euler method is used to deal with the temporal first-order derivative, and the weighted and shifted Grunwald formula is employed to discretize the distributed-order time-fractional derivative. Galerkin FEM is used for discretization of the spatial direction, and then an ADI Galerkin finite element scheme is constructed. The stability and L-2-norm convergence are proved. Several numerical experiments are provided to verify our theoretical analysis. (C) 2020 Elsevier Ltd. All rights reserved.