Mixed methods for compressible miscible displacement with the effect of molecular dispersion

Abstract

We consider a nonlinear parabolic system describing compressible miscible displacement in a porous medium[4]. Continuous time and discrete time Galerkin methods are introduced to approximate the solution, and optimalH 1-error estimates are obtained. This paper improves upon previously derived estimates in two aspects. Firstly, error estimates are given with no restrictions on the diffusion tensor. That is, we have included the effects of molecular diffusion and dispersion. Secondly, the complete compressible case is considered in the error analysis.