Journal of Scientific Computing

, Volume 22, Issue 1–3, pp 371–384 | Cite as

Block Preconditioners for LDG Discretizations of Linear Incompressible Flow Problems

  • Kanschat GuidoEmail author


We present a block preconditioner for LDG discretizations of Stokes equations. The dependence of its performance on the discretization parameters is investigated. An extension to Oseen equations is shown, yielding efficient and robust solvers in a wide regime of Reynolds numbers.


Preconditioners saddle-point problems Stokes equations Oseen equations discontinuous Galerkin finite elements 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Arnold, D. N., Brezzi, F., Cockburn, B., Marini, D. 2001Unified analysis of discontinuous Galerkin methods for elliptic problemsSIAM J. Numer. Anal.3917491779Google Scholar
  2. Bangerth, W., Hartmann, R., and Kanschat, G. (2004). deal.II Differential Equations Analysis Library, Technical Reference., 5.0 edition (first edition 1999).Google Scholar
  3. Bangerth, W., and Kanschat, G. (1999). Concepts for object-oriented finite element software – the deal.II library. Preprint 43, SFB 359, Heidelberg.Google Scholar
  4. Castillo, P., Cockburn, B., Perugia, I., Schötzau, D. 2000An a priori error estimate of the local discontinuous Galerkin method for elliptic problemsSIAM J. Numer. Anal.3816761706Google Scholar
  5. Cockburn, B., Kanschat, G., Schötzau, D. 2003LDG methods for Stokes flow problems. ENUMATH 2001Brezzi,  F. Buffa,  A. Corsaro,  S. Murli,  A. eds. Numerical Mathematics and Advanced ApplicationsSpringer ItaliaMilano755764Google Scholar
  6. Cockburn, B., Kanschat, G., Schötzau, D., Schwab, C. 2002Local discontinuous Galerkin methods for the Stokes systemSIAM J. Numer. Anal.40319343CrossRefGoogle Scholar
  7. Cockburn,  B., Shu,  C.-W. 1998The local discontinuous Galerkin method for time-dependent convection–diffusion systemsSIAM J. Numer. Anal.3524402463CrossRefGoogle Scholar
  8. Elman,  H. C., Silvester,  D. J., Wathen,  A. J. 2002Performance and analysis of saddle point preconditioners for the discrete steady-state Navier–Stokes equationsNumer. Math.90665688CrossRefGoogle Scholar
  9. Gopalakrishnan,  J., Kanschat,  G. 2003Application of unified DG analysis to preconditioning DG methodsBathe, K. J. eds. Computational Fluid and Solid Mechanics 2003ElsevierAmsterdam19431945Google Scholar
  10. Gopalakrishnan, J., Kanschat, G. 2003Multi-level preconditioners for the interior penalty method. ENUMATH 2001Brezzi,  F. Buffa,  A. Corsaro,  S. Murli,  A. eds. Numerical Mathematics and Advanced ApplicationsSpringer ItaliaMilano795804Google Scholar
  11. Gopalakrishnan, J., Kanschat, G. 2003A multilevel discontinuous Galerkin methodNumer. Math.95527550CrossRefGoogle Scholar
  12. Hackbusch,  W., Probst,  T. 1997Downwind Gauss–Seidel smoothing for convection dominated problemsNumer. Linear Algebra Appl.485102CrossRefGoogle Scholar
  13. Kanschat,  G. 2003Preconditioning discontinuous Galerkin saddle point systemsBathe, K. J. eds. Computational Fluid and Solid Mechanics 2003ElsevierAmsterdam20162018Google Scholar
  14. Kanschat, G. 2003Preconditioning methods for local discontinuous Galerkin discretizationsSIAM J. Sci. Comput.25815831CrossRefGoogle Scholar
  15. Kay,  D., Loghin,  D., Wathen,  A. J. 2002A preconditioner for the steady-state Navier–Stokes equationsSIAM J. Sci. Comput.24237256CrossRefGoogle Scholar
  16. Klawonn, A. 1998Block-triangular preconditioners for saddle point problems with a penalty termSIAM J. Sci. Comput.19172184CrossRefGoogle Scholar
  17. Murphy, M. F., Golub, G. H., Wathen, A. J. 2000A note on preconditioning for indefinite linear systemsSIAM J. Sci. Comput.2119691972CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Institut für Angewandte MathematikUniversitat HeidelbergHeidelbergGermany

Personalised recommendations