Compact and stable discontinuous Galerkin methods for convection-diffusion problems

Article English OPEN
Brdar, S.; Dedner, Andreas; Klöfkorn, R.;
(2012)

We present a new scheme, the compact discontinuous Galerkin 2 (CDG2) method, for solving nonlinear convection-diffusion problems together with a detailed comparison to other well-accepted DG methods. The new CDG2 method is similar to the CDG method that was recently int... View more
  • References (40)
    40 references, page 1 of 4

    [1] M. Ainsworth and R. Rankin, Constant free error bounds for nonuniform order discontinuous Galerkin finite-element approximation on locally refined meshes with hanging nodes, IMA J. Numer. Anal., 31 (2011), pp. 254-280.

    [2] D. N. Arnold, F. Brezzi, B. Cockburn, and L. D. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM J. Numer. Anal., 39 (2002), pp. 1749-1779.

    [3] S. Balay, J. Brown, K. Buschelman, V. Eijkhout, W. Gropp, D. Kaushik, M. Knepley, L. Curfman McInnes, B. Smith, and H. Zhang, PETSc Users Manual, Technical Report ANL-95/11 - Revision 3.1, Argonne National Laboratory, Argonne, IL, 2010.

    [4] F. Bassi and S. Rebay, A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations, J. Comput. Phys., 131 (1997), pp. 267-279.

    [5] F. Bassi, S. Rebay, G. Mariotti, S. Pedinotti, and M. Savini, A high-order accurate discontinuous finite element method for inviscid turbomachinery flows, in Proceedings of the 2nd European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, Technologisch Instituut, Antwerp, Belgium, 1997, pp. 99-108.

    [6] P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klo¨fkorn, R. Kornhuber, M. Ohlberger, and O. Sander, A generic grid interface for parallel and adaptive scientific computing. II. Implementation and tests in DUNE, Computing, 82 (2008), pp. 121- 138.

    [7] P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klo¨fkorn, M. Ohlberger, and O. Sander, A generic grid interface for parallel and adaptive scientific computing. I. Abstract framework, Computing, 82 (2008), pp. 103-119.

    [8] F. Brezzi, G. Manzini, D. Marini, P. Pietra, and A. Russo, Discontinuous Galerkin approximations for elliptic problems, Numer. Methods Partial Differential Equations, 16 (2000), pp. 365-378.

    [9] E. Burman and A. Ern, Implicit-Explicit Runge-Kutta Schemes and Finite Elements with Symmetric Stabilization for Advection-Diffusion Equations, preprint, 2010; available online at http://hal.archives-ouvertes.fr/hal-00530378/fr/.

    [10] E. Burman and P. Zunino, A domain decomposition method based on weighted interior penalties for advection-diffusion-reaction problems, SIAM J. Numer. Anal., 44 (2006), pp. 1612- 1638.

  • Metrics
Share - Bookmark