A combined method consisting of mixed finite element method (MFEM) for the pressure equation and expanded mixed finite element method with characteristics(CEMFEM) for the concentration equation is presented to solve the coupled system of incompressible miscible displacement problem. To solve the resulting nonlinear system of equations efficiently, the two‐grid algorithm relegates all of the Newton‐like iterations to grids much coarser than the original one, with no loss in order of accuracy. It is shown that coarse space can be extremely coarse and our algorithm achieve asymptotically optimal approximation when the mesh sizes satisfy $H=O(h^{\frac{1}{4}})$. Numerical experiment is provided to confirm our theoretical results.

中文翻译：

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混合位移问题的特征扩展混合有限元解的两网格方法

提出了一种求解压力方程的混合有限元方法和针对浓度方程的具有特征的扩展混合有限元方法（CEMFEM）的组合方法，以解决不可压缩的混相位移问题。为了有效地解决由此产生的非线性方程组，两网格算法将所有类似牛顿的迭代都归为比原始网格粗得多的网格，并且不损失准确性。结果表明，当网格尺寸满足时，粗糙空间可能非常粗糙，并且我们的算法实现了渐近最优逼近$H=Ø（H^{\frac{\mathrm{1个}}{4}}）$。数值实验证实了我们的理论结果。