Convergence Analysis of a Nonconforming Virtual Element Method for Compressible Miscible Displacement Problems in Porous Media

Abstract

This article presents a priori error estimates for the miscible displacement of one compressible fluid by another in a porous medium. The study utilizes the conforming virtual element method (VEM) for the approximation of the velocity, while a non‐conforming virtual element approach is employed for the concentration. The pressure is discretized using the standard piecewise discontinuous polynomial functions. These spatial discretization techniques are combined with a backward Euler difference scheme for time discretization. Error estimates are established for velocity, pressure, and concentration. The article also includes numerical results that validate the theoretical estimates.