A Priori Error Estimates of a Combined Mixed Finite Element and Discontinuous Galerkin Method for Compressible Miscible Displacement with Molecular Diffusion and Dispersion (Journal of Computational Mathematics, 2018)
A combined approximation for a kind of compressible miscible displacement problems including molecular diffusion and dispersion in porous media is studied. Mixed finite element method is applied to the flow equation, and the transport one is solved by the symmetric interior penalty discontinuous Galerkin method (SIPG). To avoid the inconvenience of the cut-off operator in [3,21], some induction hypotheses different from the ones in [6] are used. Based on interpolation projection properties, a priori $hp$ error estimates are obtained. Comparing with the existing error analysis that only deals with the diffusion case, the current work is more complicated and more significant.
Keywords: A priori error; Mixed finite element; Discontinuous Galerkin; Compressible miscible displacement.