@Article{IJNAM-17-3,
author = {Weiwei, Sun and Wu, Chengda},
title = {Efficient Galerkin-Mixed FEMs for Incompressible Miscible Flow in Porous Media},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2020},
volume = {17},
number = {3},
pages = {350--367},
abstract = {<p style="text-align: justify;">The paper focuses on numerical study of the incompressible miscible flow in porous
media. The proposed algorithm is based on a fully decoupled and linearized scheme in the temporal
direction, classical Galerkin-mixed approximations in the FE space ($V^r_h$, $S^{r-1}_h$&nbsp;× $H^{r-1}_h$) ($r$ ≥
1) in the spatial direction and a post-processing technique for the velocity/pressure, where $V^r_h$<sub>&nbsp;</sub>and $S^{r-1}_h$&nbsp;× $H^{r-1}_h$&nbsp;denotes the standard $C^0$&nbsp;Lagrange FE and the Raviart-Thomas FE spaces,
respectively. The decoupled and linearized Galerkin-mixed FEM enjoys many advantages over
existing methods. At each time step, the method only requires solving two linear systems for
the concentration and velocity/pressure. Analysis in our recent work [37] shows that the classical
Galerkin-mixed method provides the optimal accuracy $O$($h^{r+1}$) for the numerical concentration
in $L^2$-norm, instead of $O$($h^r$) as shown in previous analysis. A new numerical velocity/pressure
of the same order accuracy as the concentration can be obtained by the post-processing in the
proposed algorithm. Extensive numerical experiments in both two- and three-dimensional spaces,
including smooth and non-smooth problems, are presented to illustrate the accuracy and stability
of the algorithm. Our numerical results show that the one-order lower approximation to the
velocity/pressure does not influence the accuracy of the numerical concentration, which is more
important in applications.</p>},
issn = {2617-8710},
doi = {https://doi.org/2020-IJNAM-16863},
url = {https://global-sci.com/article/83023/efficient-galerkin-mixed-fems-for-incompressible-miscible-flow-in-porous-media}
}