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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.
}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1006-m2991}, url = {http://global-sci.org/intro/article_detail/jcm/8466.html} }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.