Nonconforming virtual element method for an incompressible miscible displacement problem in porous media

Abstract

This article presents a priori error estimates of the miscible displacement of one incompressible fluid by another through a porous medium characterized by a coupled system of nonlinear elliptic and parabolic equations. The study utilizes the $H\left(\mathrm{div}\right)$ conforming virtual element method for the approximation of the velocity, while a non-conforming virtual element approach is employed for the concentration. The pressure is discretised using the standard piecewise discontinuous polynomial functions. These spatial discretization techniques are combined with a backward Euler difference scheme for time discretization. The article also includes numerical results that validate the theoretical estimates presented.