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This article presents a priori error estimates of the miscible displacementof one incompressible fluid by another through a porous medium characterized bya coupled system of nonlinear elliptic and parabolic equations. The studyutilizes the $H(\rm{div})$ conforming virtual element method (VEM) for theapproximation of the velocity, while a non-conforming virtual element approachis employed for the concentration. The pressure is discretised using thestandard piecewise discontinuous polynomial functions. These spatialdiscretization techniques are combined with a backward Euler difference schemefor time discretization. The article also includes numerical results thatvalidate the theoretical estimates presented.

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