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((Delta t)(2-alpha) + N-r) is proved for the (r - 1)th-order finite element method (r >= 2). (C) 2011 Elsevier BM. All rights reserved.