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

Abstract

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 RT_k 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.

Keywords:

• expanded mixed finite element
• nonlinear parabolic integro-differential equations
• two-grid method
• non-Fickian flow model

2010 AMS Subject Classifications::

• 65M12
• 65M15
• 65N30

Acknowledgements

The work is supported by the National Natural Science Foundation of China (Grant No. 11171190), the Natural Science Foundation of Shandong Province (Grant No. ZR2012AM019) and the Independent Innovation Foundation of Shandong University (Grant No. 2012TS018).