A priori error analysis of a discontinuous Galerkin approximation for a kind of compressible miscible displacement problems

A kind of compressible miscible displacement problems which include molecular diffusion and dispersion in porous media are investigated. A symmetric interior penalty discontinuous Galerkin (SIPG) method is applied to the coupled system of flow and transport. Using the induction hypotheses instead of the cut-off operator and the interpolation projection properties, a priori hp error estimates are presented. The error bounds in L2(H1) norm for concentration and in L∞(L2) norm for velocity are optimal in h and suboptimal in p with a loss of power 1/2.

[1]  Yang,et al.  A UNIFIED A POSTERIORI ERROR ANALYSIS FOR DISCONTINUOUS GALERKIN APPROXIMATIONS OF REACTIVE TRANSPORT EQUATIONS 1) , 2006 .

[2]  M. Wheeler,et al.  Discontinuous Galerkin methods for coupled flow and reactive transport problems , 2005 .

[3]  B. Rivière,et al.  A Combined Mixed Finite Element and Discontinuous Galerkin Method for Miscible Displacement Problem in Porous Media , 2002 .

[4]  Jinchao Xu,et al.  Recent Progress in Computational and Applied PDES , 2002 .

[5]  Mixed methods for compressible miscible displacement with the effect of molecular dispersion , 1995 .

[6]  B. Rivière,et al.  Discontinuous Galerkin methods for flow and transport problems in porous media , 2001 .

[7]  Chen Hua,et al.  A Combined Mixed Finite Element and Discontinuous Galerkin Method for Compressible Miscible Displacement Problem , 2004 .

[8]  Mingrong Cui,et al.  Analysis of a semidiscrete discontinuous Galerkin scheme for compressible miscible displacement problem , 2008 .

[9]  Yanping Chen,et al.  A posteriori error estimation for a fully discrete discontinuous Galerkin approximation to a kind of singularly perturbed problems , 2007 .

[10]  I. Babuska,et al.  A DiscontinuoushpFinite Element Method for Diffusion Problems , 1998 .

[11]  Mary F. Wheeler,et al.  Compatible algorithms for coupled flow and transport , 2004 .

[12]  Shuyu Sun,et al.  Discontinuous Galerkin methods for reactive transport in porous media , 2003 .

[13]  Ivo Babuška,et al.  The h-p version of the finite element method , 1986 .

[14]  Jean E. Roberts,et al.  Numerical methods for a model for compressible miscible displacement in porous media , 1983 .

[15]  Béatrice Rivière,et al.  Discontinuous Galerkin methods for solving elliptic and parabolic equations - theory and implementation , 2008, Frontiers in applied mathematics.

[16]  Mary F. Wheeler,et al.  L2(H1 Norm A PosterioriError Estimation for Discontinuous Galerkin Approximations of Reactive Transport Problems , 2005, J. Sci. Comput..

[17]  Mingrong Cui,et al.  A combined mixed and discontinuous Galerkin method for compressible miscible displacement problem in porous media , 2007 .

[18]  Serge Prudhomme,et al.  A Priori error analyses of a stabilized discontinuous Galerkin method , 2003 .

[19]  Ivo Babuška,et al.  The optimal convergence rate of the p-version of the finite element method , 1987 .

[20]  Mary F. Wheeler,et al.  Discontinuous Galerkin Method for Modeling Flow and Reactive Transport in Porous Media , 2003 .