Abstract
Fractional partial differential equations (FPDEs) have many applications in areas such as diffusion processes, electromagnetics, electrochemistry, material science and turbulent flow. In recent years, people start to consider the numerical methods for solving fractional partial differential equations. The numerical methods include finite difference method, finite element method and the spectral method. In this paper, mainly consider the finite element method, for the time fractional partial differential equation. And consider time discretization. This paper obtained the optimal error estimates in time. The numerical examples demonstrate that the numerical results are consistent with the theoretical results.