Numerical Algorithms

, Volume 81, Issue 3, pp 1157–1179

# A new combined characteristic mixed finite element method for compressible miscible displacement problem

• Jiansong Zhang
Original Paper

## Abstract

A new combined characteristic mixed finite element method is developed for solving compressible miscible displacement in porous media. In this algorithm, the splitting mixed finite element (SMFE) method is applied for solving the parabolic-type pressure equation, and the mass-conservative characteristic (MCC) finite element method is applied for solving the convection-diffusion type concentration equation. The application of the splitting mixed element method results in a symmetric positive definite coefficient matrix of the separated mixed element system, while the mass-conservative characteristic finite element method not only does well in handling convection-dominant diffusion problem but also keeps mass balance. The convergence of this method is considered and the optimal L2-norm error estimate is also derived. Finally, some numerical examples are provided to confirm our theoretical analysis.

## Keywords

The method of characteristics Mass-conservative Splitting system Error estimate Miscible displacement problem

## Mathematics Subject Classification (2010)

65M12 65M15 65M25 65M60

## Notes

### Funding information

This work was supported partially by the National Natural Science Foundation of China (grant number 11401588), the Natural Science Foundation of Shandong Province (grant number ZR2014AQ005), and the Fundamental Research Funds for the Central Universities(grant number 17CX02043).

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