Least squares preconditioners for stabilized discretizations of the Navier-Stokes equations

SIAM Journal on Scientific Computing

Volumn 30, Issue 1, 2007, Pages 290-311

  Elman, Howard ^a   Howle, Victoria E ^b   Shadid, John ^c   Silvester, David ^d   Tuminaro, Ray ^b  

^a University of Maryland ^*  (United States)

^b SANDIA NATIONAL LABORATORIES   (United States)

^c SANDIA NATIONAL LABORATORIES   (United States)

^d UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Iterative algorithms; Navier Stokes; Preconditioning

Indexed keywords

FINITE ELEMENT METHOD; ITERATIVE METHODS; VISCOUS FLOW;

DISCRETIZATIONS; INCOMPRESSIBLE (NAVIER )STOKES EQUATION; INCOMPRESSIBLE NAVIER STOKES EQUATIONS; ITERATIVE ALGORITHM; LEAST SQUARE; LOW ORDER; NAVIER STOKES; NAVIER-STOKES EQUATION; PRECONDITIONERS; PRECONDITIONING;

NAVIER STOKES EQUATIONS;

EID: 55549136763     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/060655742     Document Type: Article

References (18)

1. B. BECKERMANN AND S. SERRA-CAPIZZANO, On the asymptotic spectrum of finite element matrix sequences, SIAM J. Numer. Anal., 45 (2007), pp. 746-769.
2. P. B. BOCHEV, C. R. DOHRMANN, AND M. D. GUNZBURGER, Stabilization of low-order mixed finite elements for the Stokes equations, SIAM J. Numer. Anal., 44 (2006), pp. 82-101.
3. J. M. BOLAND AND R. A. NICOLAIDES, Stability of finite elements under divergence constraints, SIAM J. Numer. Anal, 20 (1983), pp. 722-731.
4. F. BREZZI AND M. FORTIN, Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991.
5. H. C. ELMAN, Preconditioning for the steady-state Navier-Stokes equations with low viscosity, SIAM J. Sci. Comput., 20 (1999), pp. 1299-1316.
6. H. ELMAN, V. E. HOWLE, J. SHADID, R. SHUTTLEWORTH, AND R. TUMINARO, Block preconditioners based on approximate commutators, SIAM J. Sci. Comput., 27 (2006), pp. 1651-1668.
7. H. C. ELMAN, D. J. SILVESTER, AND A. J. WATHEN, Finite Elements and Fast Iterative Solvers, Oxford University Press, Oxford, UK, 2005.
8. P. M. GRESHO AND R. SANI, Incompressible Flow and the Finite Element Method: Isothermal Laminar Flow, Wiley, Chichester, UK, 1998.
9. T. J. HUGHES AND L. P. FRANCA, A new finite element formulation for computational fluid dynamics: VII. The Stokes problem with various well-posed boundary conditions: Symmetric formulations that converge for all velocity/pressure spaces, Comput. Methods Appl. Mech. Engrg., 65 (1987), pp. 85-96.
10. D. KAY, D. LOGHIN, AND A. WATHEN, A preconditioner for the steady-state Navier-Stokes equations, SIAM J. Sci. Comput., 24 (2002), pp. 237-256.
11. D. KAY AND D. SILVESTER, A posteriori error estimation for stabilized mixed approximations of the Stokes equations, SIAM J. Sci. Comput., 21 (1999), pp. 1321-1336.
12. N. KECHKAR AND D. SILVESTER, Analysis of locally stabilized mixed finite element methods for the Stokes problem, Math. Comp., 58 (1992), pp. 1-10.
13. D. SILVESTER, H. ELMAN, D. KAY, AND A. WATHEN, Efficient preconditioning of the linearized Navier-Stokes equations for incompressible flow, J. Comput. Appl. Math., 128 (2001), pp. 261-279.
14. D. J. SILVESTER, H. C. ELMAN, AND A. RAMAGE, IFISS: Incompressible Flow Iterative Solution Software, available online at http://www.manchester.ac.uk/ifiss.
15. B. SMITH, P. BJØRSTAD, AND W. GROPP, Domain Decomposition, Cambridge University Press, Cambridge, UK, 1996.
16. R. STENBERG, Analysis of mixed finite element methods for the Stokes problem: A unified approach, Math. Comp., 42 (1984), pp. 9-23.
17. G. STOYAN, Towards discrete Velte decompositions and narrow bounds for inf-sup constants, Comput. Math. Appl., 38 (1999), pp. 243-261.
18. A. J. WATHEN, Realistic eigenvalue bounds for the Galerkin mass matrix, IMA J. Numer. Anal., 7 (1987), pp. 449-457.