A new mixed element method for a class of time-fractional partial differential equations

Abstract

A kind of new mixed element method for time-fractional partial differential equations is studied. The Caputo-fractional derivative of time direction is approximated by two-step difference method and the spatial direction is discretized by a new mixed element method, whose gradient belongs to the simple L 2 Ω 2 space replacing the complex H (d i v; Ω) space. Some a priori error estimates in L 2 -norm for the scalar unknown u and in L 2 2 -norm for its gradient σ. Moreover, we also discuss a priori error estimates in H 1 -norm for the scalar unknown u. © 2014 Yang Liu et al.