A two-grid expanded mixed element method for nonlinear non-Fickian flow model in porous media

The full discrete scheme of expanded mixed finite element approximation is introduced for nonlinear parabolic integro-differential equations modelling non-Fickian flow in porous media. To solve the nonlinear problem efficiently, a two-grid algorithm is considered and analysed. This approach allows us to perform all of the nonlinear iterations on a coarse grid space and just execute a linear system on a fine grid space. Based on RTk mixed element space, error estimates and convergence results are presented for solutions of the two-grid method. Some numerical examples are given to verify the theoretical predictions and show the efficiency of the two-grid method.