Analysis of Lowest-Order Characteristics-Mixed FEMs for Incompressible Miscible Flow in Porous Media

Unconditional Convergence and Optimal Error Estimates of a Galerkin-Mixed FEM for Incompressible Miscible Flow in Porous Media

In this paper, we study the unconditional convergence and error estimates of a Galerkin-mixed FEM with the linearized semi-implicit Euler scheme for the equations of incompressible miscible flow in porous media. We prove that the optimal L2 error estimates hold without any time-step (convergence) conditions, while all previous works require certain time-step restrictions. Our theoretical result...

Instability Analysis of Miscible Displacements in Homogeneous Porous Media

A Second Order Characteristic Method for Approximating Incompressible Miscible Displacement in Porous Media

An approximation scheme is defined for incompressible miscible displacement in porous media. This scheme is constructed by two methods. Under the regularity assumption for the pressure, cubic Hermite finite element method is used for the pressure equation, which ensures the approximation of the velocity smooth enough. A second order characteristic finite element method is presented to handle th...

Parallel Nonoverlapping DDM Combined with the Characteristic Method for Incompressible Miscible Displacements in Porous Media

Two types of approximation schemes are established for incompressible miscible displacements in porous media. First, standard mixed finite element method is used to approximate the velocity and pressure. And then parallel non-overlapping domain decomposition methods combined with the characteristics method are presented for the concentration. These methods use the characteristic method to handl...

A parallel second-order adaptive mesh algorithm for incompressible flow in porous media.

In this paper, we present a second-order accurate adaptive algorithm for solving multi-phase, incompressible flow in porous media. We assume a multi-phase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting, the total velocity, defined to be the sum of the p...