The stability of the two-dimensional incompressible mmiscible displacement in porous media using the Petrov Galerkin finite element method

Abstract

A two-dimensional displacement fluid in a porous material that is incompressible and immiscible is studied via the lens of a nonlinear system of two pair partial differential equations models. A petrov Galerkin mixed finite element approach is used to estimate the mixture's pressure and Darcy velocity, while a petrov Galerkin Finite Element Method (PGFEM) is stability prove for the pressure, velocity and Saturation.