The numerical methods for miscible displacment in aggregated or sorbing medium are considered. A mixed finite element method is adopted for the pressure equation. The concentration in the mobile water is approximated by a combination of a Galerkin finite element method and the method of characteristics and the concentration in immobile water is approximated by a standard Galerkin method. The moving mesh technique which depends on time t is adopted here. The moving meshes can vary in different spacial domains with different variable times. Optima error estimates in energy norm and L2 norm are obtained under certain constraints.
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