Fully-Discrete For Expanded H^1-Galerkin Mixed Finite Element Method of PIDEs With Nonlinear Memory

Abstract

In this paper, the expanded -Galerkin mixed finite element method is proposed for parabolic integro-differential equations with nonlinear memory. The fully discrete error estimates based on backward Euler method are obtained. Moreover, the optimal a priori error estimates in  and -norm for the scalar unknown  and the error results in -norm for  gradient , and its flux  are derived. Finally, numerical results are presented to confirm our theoretical analysis.