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Keywords:

  • compressible;
  • discontinuous Galerkin method;
  • full-discrete;
  • mixed finite element;
  • superconvergence

Abstract

An efficient time-stepping procedure is investigated for a two-dimensional compressible miscible displacement problem in porous media in which the mixed finite element method with Raviart-Thomas space is applied to the flow equation, and the transport one is solved by the symmetric interior penalty discontinuous Galerkin approximation on Cartesian meshes. Based on the projection interpolations and the induction hypotheses, a superconvergence error estimate is obtained. During the analysis, an extension of the Darcy velocity along the Gauss line is also used in the evaluation of the coefficients in the Galerkin procedure for the concentration. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013