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 $H(\rm{div})$ 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. The article also includes numerical results that validate the theoretical estimates presented.

翻译：本文针对多孔介质中一种不可压缩流体被另一种流体驱替的互溶驱替问题，建立了先验误差估计。该问题由非线性椭圆和抛物型耦合方程组表征。研究采用$H(\rm{div})$协调虚拟元方法（VEM）近似速度场，同时使用非协调虚拟元方法处理浓度场。压力采用标准分片间断多项式函数进行离散。这些空间离散技术与时间离散中的向后欧拉差分格式相结合。文中还通过数值结果验证了所提出的理论估计。