A two-grid stabilization method for solving the steady-state Navier-Stokes equations

Numerical Methods for Partial Differential Equations

Volumn 22, Issue 3, 2006, Pages 728-743

  Kaya, Songul ^a   Rivière, Béatrice ^a  

^a UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

Finite elements; Navier Stokes equations; Subgrid eddy viscosity; Two grid method

Indexed keywords

EID: 33646267926     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20120     Document Type: Article

References (21)

1. 1 J. Xu, Two‐grid discretization techniques for linear and nonlinear PDE, SIAM J Numer Anal 33 (1996), 1759–1777.
2. 2 M. Marion and J. Xu, Error estimates for a new nonlinear Galerkin method based on two‐grid finite elements, SIAM J Numer Anal 32 (1995), 1170–1184.
3. 3 V. Girault and J.‐L. Lions, Two‐grid finite element schemes for the steady Navier‐Stokes problem in polyhedra, Portugal Math 58 (2001), 25–57.
4. 4 V. Girault and J.‐L. Lions, Two‐grid finite element schemes for the transient Navier‐Stokes, Math Modelling Num Anal 35 (2001), 945–980.
5. 5 M. Fortin, R. Guenette, and R. Pierre, Numerical analysis of the modified EVSS method, Comp Meth Appl Mech Eng 143 (1997), 79–95.
6. 6 J. L. Guermond, Stabilization of Galerkin approximations of transport equations by subgrid modelling, M2AN 33 (1999), 1293–1316.
7. 7 W. J. Layton, A connection between subgrid scale eddy viscosity and mixed methods, Appl Math Comput 133 (2002), 147–157.
8. 8 S. Kaya and W. J. Layton, Subgrid‐scale eddy viscosity methods are variational multiscale methods, Technical report, TR‐MATH 03‐05, University of Pittsburgh, 2003.
9. 9 T. J. R. Hughes, The multiscale phenomena: Green's functions, the Dirichlet‐to‐Neumann formulation, subgrid‐scale models, bubbles and the origin of stabilized methods, Computer Methods Appl Mech Eng 127 (1995), 387–401.
10. 10 V. John and S. Kaya, Finite element error analysis and implementation of a variational multiscale method for the Navier Stokes equations, SIAM J Sci Comput (2004), accepted for publication.
11. 11 S. Kaya and B. Rivière, A discontinuous subgrid eddy viscosity method for the time‐dependent Navier Stokes equations, SIAM J Numer Anal (2005), accepted for publication.
12. 12 R. A. Adams, Sobolev spaces, Academic Press, New York, 1975.
13. 13 G. Duvaut and J. L. Lions, Inequalities in mechanics and physics, Springer‐Verlag, New York, 1976.
14. 14 V. Girault and P. A. Raviart, Finite element approximation of the Navier‐Stokes equations, Springer‐Verlag, Berlin, 1979.
15. 15 D. N. Arnold, F. Brezzi, and M. Fortin, A stable finite element for the Stokes equations, Calcolo 21 (1984), 337–344.
16. 16 M. Gunzburger, Finite element methods for viscous incompressible flows: a guide to theory, practice and algorithms, Academic Press, Boston, 1989.
17. 17 M. Fortin, Old and new finite elements for incompressible flows, Int J Num Meth Fluids 1 (1981), 347–364.
18. 18 M. Crouzeix and P. A. Raviart, Conforming and nonconforming finite element methods for solving Stokes equations, RAIRO Anal Numer 7 (1973), 33–36.
19. 19 P. Sonneveld, A fast Lanczos‐type solver for nonsymmetric linear systems, SIAM J Sci Stat Comput 10 (1989), 36–52.
20. 20 U. Ghia, K. N. Ghia, and C. T. Shin, High resolutions for incompressible flows using the Navier‐Stokes equations and a multigrid method, J Comput Phys 48 (1982), 387–411.
21. 21 J. E. Akin, Finite element for analysis and design, Academic Press, San Diego, 1994.