Abstract
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.
Similar content being viewed by others
References
D. N. Arnold F. Brezzi B. Cockburn D. Marini (2001) ArticleTitleUnified analysis of discontinuous Galerkin methods for elliptic problems SIAM J. Numer. Anal. 39 IssueID5 1749–1779
Bangerth, W., Hartmann, R., and Kanschat, G. (2004). deal.II Differential Equations Analysis Library, Technical Reference. www.dealii.org, 5.0 edition (first edition 1999).
Bangerth, W., and Kanschat, G. (1999). Concepts for object-oriented finite element software – the deal.II library. Preprint 43, SFB 359, Heidelberg.
P. Castillo B. Cockburn I. Perugia D. Schötzau (2000) ArticleTitleAn a priori error estimate of the local discontinuous Galerkin method for elliptic problems SIAM J. Numer. Anal. 38 IssueID5 1676–1706
B. Cockburn G. Kanschat D. Schötzau (2003) LDG methods for Stokes flow problems. ENUMATH 2001 F. Brezzi A. Buffa S. Corsaro A. Murli (Eds) Numerical Mathematics and Advanced Applications Springer Italia Milano 755–764
B. Cockburn G. Kanschat D. Schötzau C. Schwab (2002) ArticleTitleLocal discontinuous Galerkin methods for the Stokes system SIAM J. Numer. Anal. 40 IssueID1 319–343 Occurrence Handle10.1137/S0036142900380121
B. Cockburn C.-W. Shu (1998) ArticleTitleThe local discontinuous Galerkin method for time-dependent convection–diffusion systems SIAM J. Numer. Anal. 35 2440–2463 Occurrence Handle10.1137/S0036142997316712
H. C. Elman D. J. Silvester A. J. Wathen (2002) ArticleTitlePerformance and analysis of saddle point preconditioners for the discrete steady-state Navier–Stokes equations Numer. Math. 90 IssueID4 665–688 Occurrence Handle10.1007/s002110100300
J. Gopalakrishnan G. Kanschat (2003) Application of unified DG analysis to preconditioning DG methods K. J. Bathe (Eds) Computational Fluid and Solid Mechanics 2003 Elsevier Amsterdam 1943–1945
J. Gopalakrishnan G. Kanschat (2003) Multi-level preconditioners for the interior penalty method. ENUMATH 2001 F. Brezzi A. Buffa S. Corsaro A. Murli (Eds) Numerical Mathematics and Advanced Applications Springer Italia Milano 795–804
J. Gopalakrishnan G. Kanschat (2003) ArticleTitleA multilevel discontinuous Galerkin method Numer. Math. 95 IssueID3 527–550 Occurrence Handle10.1007/s002110200392
W. Hackbusch T. Probst (1997) ArticleTitleDownwind Gauss–Seidel smoothing for convection dominated problems Numer. Linear Algebra Appl. 4 IssueID2 85–102 Occurrence Handle10.1002/(SICI)1099-1506(199703/04)4:2<85::AID-NLA100>3.0.CO;2-2
G. Kanschat (2003) Preconditioning discontinuous Galerkin saddle point systems K. J. Bathe (Eds) Computational Fluid and Solid Mechanics 2003 Elsevier Amsterdam 2016–2018
G. Kanschat (2003) ArticleTitlePreconditioning methods for local discontinuous Galerkin discretizations SIAM J. Sci. Comput. 25 IssueID3 815–831 Occurrence Handle10.1137/S1064827502410657
D. Kay D. Loghin A. J. Wathen (2002) ArticleTitleA preconditioner for the steady-state Navier–Stokes equations SIAM J. Sci. Comput. 24 IssueID1 237–256 Occurrence Handle10.1137/S106482759935808X
A. Klawonn (1998) ArticleTitleBlock-triangular preconditioners for saddle point problems with a penalty term SIAM J. Sci. Comput. 19 IssueID1 172–184 Occurrence Handle10.1137/S1064827596303624
M. F. Murphy G. H. Golub A. J. Wathen (2000) ArticleTitleA note on preconditioning for indefinite linear systems SIAM J. Sci. Comput. 21 IssueID6 1969–1972 Occurrence Handle10.1137/S1064827599355153
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Guido, K. Block Preconditioners for LDG Discretizations of Linear Incompressible Flow Problems. J Sci Comput 22, 371–384 (2005). https://doi.org/10.1007/s10915-004-4144-6
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10915-004-4144-6