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 L2Ω2 space replacing the complex H(div;Ω) space. Some a priori error estimates in L2-norm for the scalar unknown u and in L22-norm for its gradient σ. Moreover, we also discuss a priori error estimates in H1-norm for the scalar unknown u.