::title::A Priori Error Estimates of a Combined Mixed Finite Element and Discontinuous Galerkin Method for Compressible Miscrible Displacement with Molecular Diffusion and Dispersion
::author::1::Jiming Yang
::author::2::Yanping Chen
::address::1::College of Science, Hunan Institute of Engineering, Xiangtan 411104, China
::address::2::School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
::email::yangjiminghnie@163.com, ypchen@xtu.edu.cn, yanpingchen@scnu.edu.cn
::receive::Received 2008-12-6 Accepted 2010-2-4
::online::Available online 2010-9-20
::DOI::10.4208/jcm.1006-m2991
::keywords::A priori error, Mixed finite element, Discontinuous Galerkin,
Compressible miscible displacement.
::ams::65M12, 65M60.
::abstract::
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 \cite{p1,p15},
some induction hypotheses 
different from the ones in \cite{p18} 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.