A New Mixed Element Method for a Class of Time-Fractional Partial Differential Equations

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(div; 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.