An Alternating Direction Galerkin Method Combined with a Modified Method of Characteristics for Miscible Displacement Influenced by Mobile and Immobile Water

Abstract

Numerical approximations are considered for a mathematical model for miscible displacement influenced by mobile and immobile water. A mixed finite element method is adopted to give a direct approximation of the velocity, the concentration in mobile water is approximated by an alternating direction Galerkin finite element method combined with the method of characteristics and the concentration in immobile water is approximated by a standard Galerkin method. Optimal order $L^2$- and $H^1$-error estimates are derived.