论文标题
对多孔介质中不可压缩的混乱流的Galerkin-Mixed Fem的新分析
New analysis of Galerkin-mixed FEMs for incompressible miscible flow in porous media
论文作者
论文摘要
在过去的几十年中，已经对多孔介质中不可压缩的混杂流量进行了不可压缩的混溶性流量的分析。在实际应用中特别感兴趣的是最低级的Galerkin混合方法，{其中使用线性拉格朗日Fe近似用于浓度，而最低级的raviart-thomas fe近似用于速度/压力。先前的作品仅在空间方向上显示了该方法的一阶准确度，但是，这在时间步长和空间网格上都不是最佳且无效的。在本文中，我们为在一般情况下为所有三个组件的Galerkin-Mixed FEM提供了新的$ L^2 $ norm错误估计。特别是，对于最低级的galerkin混合fem，我们无条件地显示了浓度$ l^2 $ -norm}的二阶{精度。提出了两个和三维模型的数值结果，以确认我们的理论分析。更重要的是，我们的方法可以扩展到许多强耦合系统的混合FEM分析，以获得所有组件的最佳误差估计。
Analysis of Galerkin-mixed FEMs for incompressible miscible flow in porous media has been investigated extensively in the last several decades. Of particular interest in practical applications is the lowest-order Galerkin-mixed method, { in which a linear Lagrange FE approximation is used for the concentration and the lowest-order Raviart-Thomas FE approximation is used for the velocity/pressure. The previous works only showed the first-order accuracy of the method in $L^2$-norm in spatial direction,} which however is not optimal and valid only under certain extra restrictions on both time step and spatial mesh. In this paper, we provide new and optimal $L^2$-norm error estimates of Galerkin-mixed FEMs for all three components in a general case. In particular, for the lowest-order Galerkin-mixed FEM, we show unconditionally the second-order { accuracy in $L^2$-norm} for the concentration. Numerical results for both two and three-dimensional models are presented to confirm our theoretical analysis. More important is that our approach can be extended to the analysis of mixed FEMs for many strongly coupled systems to obtain optimal error estimates for all components.
