A Posteriori Error Estimates of a Combined Mixed Finite Element and Discontinuous Galerkin Method for a Kind of Compressible Miscible Displacement Problems (Advances in Applied Mathematics and Mechanics, 2013)
A kind of compressible miscible displacement problems which includemolecular diffusion and dispersion in porous media are investigated.The mixed finite element method is applied to the flow equation, and thetransport one is solved by the symmetric interior penaltydiscontinuous Galerkin method. Based on a duality argument,employing projection estimates and approximation properties, aposteriori residual-type $hp$ error estimates for the coupled systemare presented, which is often used for guiding adaptivity. Comparingwith the error analysis carried out by Yang (Int. J. Numer. Meth.Fluids, 65(7) (2011), pp. 781-797), the current work is morecomplicated and challenging.