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 ( ( Δ t ) 2 − α + N − r ) is proved for the ( r − 1 ) th-order finite element method ( r ≥ 2 ) .