High-order finite element methods for time-fractional partial differential equations

The aim of this paper is to develop high-order methods for solving time-fractional partial differential equations. The proposed high-order method is based on high-order finite element method for space and finite difference method for time. Optimal convergence rate O((Δt)2−α+N−r)O((Δt)2−α+N−r) is proved for the (r−1)(r−1)th-order finite element method (r≥2)(r≥2).