In this article, we propose a combined hybrid discontinuous mixed finite element method for miscible displacement problem with local discontinuous Galerkin method. Here, to obtain more accurate approximation and deal with the discontinuous case, we use the hybrid mixed element method to approximate the pressure and velocity, and use the local discontinuous Galerkin finite element method for the concentration. Compared with other combined methods, this method can improve the efficiency of computation, deal with the discontinuous problem well and keep local mass balance. We study the convergence of this method and give the corresponding optimal error estimates in L^∞(L²) for velocity and concentration and the super convergence in L^∞(H¹) for pressure. Finally, we also present some numerical examples to confirm our theoretical analysis.

中文翻译：

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局部不连续Galerkin法求解不可压缩混溶位移问题的混合混合元法

在本文中，我们提出了一种混合混合不连续混合有限元方法和局部不连续Galerkin方法，解决了混溶位移问题。在这里，为了获得更准确的近似值并处理不连续的情况，我们使用混合混合元法来近似压力和速度，并使用局部不连续的Galerkin有限元法进行浓度计算。与其他组合方法相比，该方法可以提高计算效率，很好地处理不连续性问题，并保持局部质量平衡。我们研究了该方法的收敛性和给在相应的最优误差估计大号^∞（大号²）对于速度和浓度，并在超级收敛大号压力的^∞（H ¹）。最后，我们还提供一些数值示例来证实我们的理论分析。