EFFICIENT GALERKIN-MIXED FEMS FOR INCOMPRESSIBLE MISCIBLE FLOW IN POROUS MEDIA

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 × Η^r−1_h) (r ≥1)in the spatial direction and a post-processing technique for the velocity/pressure, where V^r_h and S^r−1_h × H^r−1_h denotes the standard C⁰ 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 L²-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.