A combined hybrid mixed element method for incompressible miscible displacement problem with local discontinuous Galerkin procedure

Abstract

In this article, we propose a combined hybrid discontinuous mixed finite element method for miscible displacement problem with local discontinuous Galerkin method. Here, to obtain more accurate approximation and deal with the discontinuous case, we use the hybrid mixed element method to approximate the pressure and velocity, and use the local discontinuous Galerkin finite element method for the concentration. Compared with other combined methods, this method can improve the efficiency of computation, deal with the discontinuous problem well and keep local mass balance. We study the convergence of this method and give the corresponding optimal error estimates in L ∞ (L 2) for velocity and concentration and the super convergence in L ∞ (H 1) for pressure. Finally, we also present some numerical examples to confirm our theoretical analysis.

A Mass-Preserving Characteristic Finite Difference Method for Miscible Displacement Problem

“…In this field, two-phase flow displacement (water and oil) is one of the most important basic problems. In this article, we will consider to construct a new numerical method for the following incompressible miscible displacement problem in porous media, which is governed by a nonlinear coupled system of partial differential equations: the pressure is governed by an elliptic equation and the concentration is governed by a convection-diffusion equation (see [1][2][3]):…”