A numerical method for solving the two-dimensional distributed order space-fractional diffusion equation on an irregular convex domain

In this paper, the two-dimensional distributed order space-fractional diffusion equation on an irregular convex domain is considered. The finite element method using unstructured mesh adapted to the irregular domain is proposed to solve the considered equation. To testify the efficiency of the proposed method, two numerical examples are given. By the error analysis and the comparison between the numerical solution and the exact solution, the finite element method applied in this paper is shown to be valid in solving the two-dimensional distributed order space-fractional diffusion equation on an irregular convex domain.