A Low Order Characteristic-nonconforming Finite Element Method For Solving A Two-phase Of Water And Oil Displacement Problem In Porous Medium

A two-phase of water and oil incompressible miscible displacement problem in porous medium is modeled by a nonlinear coupled system of two partial differential equations.The pressure equation is elliptic,while the concentration equation is parabolic but normally convection dominated.In this paper,a nonconforming characteristic finite element method is posed for this problem.Compared with the traditional Galerkin finite element method,this method can eliminate the convection item effectively,and achieve better numerical results.The constrained nonconforming rotated Q1element(CNQ₁^rot)is taken to approximate the original variables concentration and pressure.Then,based on the typical characters of CNQ₁^rot element,combining the derivative transfer and some new estimation skills,the superclose results in the broken H¹-norm of the concentration variable is derived.Finally,the global superconvergence estimate in the broken H¹-norm of the concentration variable is derived through the interpolated postprocessing technique.