Convergence analysis of a nonconforming virtual element method for compressible miscible displacement problems in porous media

Abstract

This article presents a priori error estimates of the miscible displacement of one compressible fluid by another in a porous medium. The study utilizes the $H(\mathrm{div})$ 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 discretised 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.

30 pages, 9 figures, 5 tables. arXiv admin note: substantial text overlap with arXiv:2401.01618