$$L^p$$ L p Error Estimates of Two-Grid Method for Miscible Displacement Problem

Abstract

This paper is concerned about the $$L^p$$Lp error analysis of two-grid method for incompressible miscible displacement in porous medium. A characteristics finite element method is presented for the concentration equation to handle the convection part, and standard mixed finite element is used for the pressure equation. Mixed finite element method has an advantage of approximating the unknown variable and its diffusive flux across grid-cell interfaces simultaneously, which has been proven to be an effective numerical method for solving fluid problems. Moreover, we linearize the equations based on the Newton iteration method, then, two-grid algorithm is considered in this full discrete scheme problems. It shown that coarse space can be extremely coarse and we achieve asymptotically optimal approximation. Numerical experiments are presented finally to validate the theoretical analysis.