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

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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.

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Funding

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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  1. Department of Applied Mathematics, China University of Petroleum, Qingdao, 266580, People’s Republic of China

    Jiansong Zhang

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  1. Jiansong Zhang
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Zhang, J. A new combined characteristic mixed finite element method for compressible miscible displacement problem. Numer Algor 81, 1157–1179 (2019). https://doi.org/10.1007/s11075-018-0590-3

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  • DOI: https://doi.org/10.1007/s11075-018-0590-3

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