Abstract: A standard finite element method for miscible displacement of multiphase fully compressible flow with dispersion is given and optimal error estimate in H¹-norm is derivedIn order to enhance the approximate accuracy,a modified finite element method,whose working quantity is almost the same as that of the stsndard method but whose convergent rate in L²-norm is optimal,is proposed.

Key words: multiphase compressible flow, miscible displacement, error estimate, finite element method