A new combined discontinuous Galerkin method is proposed for compressible miscible displacement problem in porous media. Here, a splitting positive definite mixed finite element method is used for the pressure and Darcy velocity, while an interior penalty discontinuous Galerkin (IPDG) method is used for the transport equation. The stability and convergence of this algorithm are considered, and the optimal a priori error estimate in $l^{\infty }\left(L^2\right)$ for velocity, pressure and concentration are given. Finally we provide some numerical results to confirm our theoretical analysis, and simulate compressible fluid flows through homogeneous and isotropic porous media.

中文翻译：

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可压缩混溶位移问题的新的不连续Galerkin混合有限元方法

针对多孔介质中的可压缩混溶位移问题，提出了一种新的组合不连续Galerkin方法。在此，将分裂正定混合有限元方法用于压力和达西速度，将内部罚分不连续伽勒金（IPDG）方法用于运输方程。考虑了该算法的稳定性和收敛性，并给出了最优的先验误差估计。${升}^{\infty }（{\mathrm{大号}}^2）$给出了速度，压力和浓度。最后，我们提供一些数值结果来证实我们的理论分析，并模拟可压缩流体流过均质和各向同性的多孔介质。