A new expanded mixed method for parabolic integro-differential equations

A new expanded mixed scheme is studied and analyzed for linear parabolic integro-differential equations. The proposed method's gradient belongs to the simple square integrable space replacing the classical H(div;Ω) space. The new expanded mixed projection is introduced, the existence and uniqueness of solution for semi-discrete scheme are proved and the fully discrete error estimates based on both backward Euler scheme are obtained. Moreover, the optimal a priori error estimates in L2 and H1-norm for the scalar unknown u and the error results in L2(Ω)-norm for its gradient λ, and its flux σ (the coefficients times the negative gradient) are derived. Finally, some numerical results are calculated to verify our theoretical analysis.