A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium. A mixed finite element method is employed to approximate the pressure and the Darcy velocity, and a characteristic finite element method is used to approximate the concentration. Twice Newton iteration is applied on the fine grid to linearize the fully discrete problem using the coarse-grid solution as the initial guess. Moreover, the L^q error estimates are conducted for the pressure, Darcy velocity, and concentration variables in the two-grid solutions. It is shown both theoretically and numerically that the coarse space can be extremely coarse, with no loss in the order of accuracy, and the two-grid algorithm still achieves the optimal approximation as long as the mesh sizes satisfy \(H = O(h^{\frac {1}{4}})\). The numerical results show that this algorithm is very effective.

中文翻译：

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可压缩混溶位移问题的特征有限元二网格算法

推导了非线性抛物线系统，以描述多孔介质中的可压缩混溶位移。使用混合有限元方法来近似压力和达西速度，而使用特征有限元方法来近似浓度。使用粗网格解决方案作为初始猜测，在细网格上应用两次牛顿迭代以线性化完全离散的问题。此外，对两个网格解决方案中的压力，达西速度和浓度变量进行L ^q误差估计。从理论和数值上都显示出，粗略空间可以是极其粗大的，没有精度方面的损失，并且只要网格大小满足要求，两网格算法仍然可以实现最佳逼近。\（H = O（h ^ {\ frac {1} {4}}）\）。数值结果表明该算法非常有效。