A combined mixed and characteristic mixed finite element method for incompressible miscible displacement problem in porous media

摘要

In this paper, an approximate scheme is defined for incompressible miscible displacement in porous media. This scheme is constructed by using characteristics mixed finite element method for concentration equation and mixed finite element method for pressure equation. Several lemmas are introduced to deal with the difficulties arising from the combination of characteristics method and mixed finite element method. An optimal-order error estimate in L²-norm for the concentration, pressure and the velocity vector is proved for general mixed finite element spaces.