A UNIFIED A POSTERIORI ERROR ANALYSIS FOR DISCONTINUOUS GALERKIN APPROXIMATIONS OF REACTIVE TRANSPORT EQUATIONS 1)

Four primal discontinuous Galerkin methods are applied to solve reactive transport problems, namely, Oden-Babuy ska-Baumann DG (OBB-DG), non-symmetric interior penalty Galerkin (NIPG), symmetric interior penalty Galerkin (SIPG), and incomplete interior penalty Galerkin (IIPG). A unified a posteriori residual-type error estimation is derived explicitly for these methods. From the computed solution and given data, explicit estimators can be computed efficiently and directly, which can be used as error indicators for adaptation. Unlike in the reference [10], we obtain the error estimators in L 2 (L 2 ) norm by using duality techniques instead of in L 2 (H 1 ) norm.

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

[2]  Mary F. Wheeler.  A Posteriori Error Estimates and Mesh Adaptation Strategy for Discontinuous Galerkin Methods Applied to Diffusion Problems , 2000 .

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

[4]  Mary F. Wheeler,et al.  A Priori Error Estimates for Finite Element Methods Based on Discontinuous Approximation Spaces for Elliptic Problems , 2001, SIAM J. Numer. Anal..

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

[6]  Alexandre Ern,et al.  A posteriori discontinuous Galerkin error estimates for transient convection-diffusion equations , 2005, Appl. Math. Lett..

[7]  Carl I. Steefel,et al.  Reactive transport in porous media , 1996 .

[8]  Timothy J. Barth,et al.  A Posteriori Error Estimation for Discontinuous Galerkin Approximations of Hyperbolic Systems , 2000 .

[9]  Claes Johnson,et al.  Discontinuous Galerkin finite element methods for second order hyperbolic problems , 1993 .

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

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

[12]  C. Dawson,et al.  Computational methods for multiphase flow and reactive transport problems arising in subsurface contaminant remediation , 1996 .