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

الملخص EN

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 .