The Finite Element Approximations for Space Fractional Diffusion Equation

In this paper, we consider the numerical solution of the space fractional diffusion equation, which is obtained from the standard diffusion equation by replacing the second-order space derivative with a fractional derivative (of order alpha, with 1 < alpha <= 2). The main purpose of this work is to construct scheme to efficiently solve the space fractional diffusion equation. We get a forward Euler scheme with finite difference method. We attain a weak formulation of finite element method from the above scheme. Convergence of the method is rigorously established. Numerical experiments are carried out to support the theoretical predictions.