A multilevel mesh independence principle for the Navier-Stokes equations

SIAM Journal on Numerical Analysis

Volumn 33, Issue 1, 1996, Pages 17-30

  Layton, W ^a,b   Lenferink, H W J ^a  

^a RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

^b UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

Mesh independence principle; Multilevel; Navier Stokes equations

Indexed keywords

EID: 0002788113     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/0733002     Document Type: Article

References (23)

1. G. ANDERSON AND X. YE, The derivation of minimal support basis functions for the discrete divergence operator, Technical rep., University of Arkansas at Little Rock, 1992.
2. O. AXELSSON, On mesh independence and Newton type methods, Department of Mathematics, Catholic University of Nijmegen, the Netherlands, 1992.
3. O. AXELSSON AND W. LAYTON, A two-level method for the discretization of nonlinear boundary value problems, SIAM J. Numer. Anal., 33 (1996), to appear.
4. J. BOLAND AND W. LAYTON, Error analysis for finite element methods for steady natural convection problems, Numer. Funct. Anal. Optim., 11 (1990), pp. 449-483.
5. P. BRADSHAW, T. CEBECI, AND J. H. WHITELAW, Engineering Calculation Methods for Turbulent Flow, Academic Press, New York, 1981.
6. P. CONSTANTIN AND C. FOIAS, Navier-Stokes Equations, University of Chicago Press, Chicago, 1988.
7. V. GIRAULT AND P.-A. RAVIART, Finite element approximation of the Navier-Stokes equations, Lecture Notes in Mathematics, Vol. 749, Springer-Verlag, Berlin, Heidelberg, New York, 1979.
8. _, Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms, Springer-Verlag, Berlin, 1986.
9. M. GUNZBURGER, Finite Element Methods for Viscous Incompressible Flows. A Guide to Theory, Practice and Algorithms, Academic Press, Boston, 1989.
10. M. D. GUNZBURGER AND J. C. TURNER, JR., An analysis of approximations of an algebraic model of turbulence, Comput. Math. Appl., 15 (1988), pp. 945-951.
11. J. O. HINZE, Turbulence, McGraw Hill, New York, 1959.
12. O. KARAKASHIAN, On a Galerkin-Lagrange multiplier method for the stationary Navier-Stokes equations, SIAM J. Numer. Anal., 19 (1982), pp. 909-923.
13. W. LAYTON, A two-level discretization method for the Navier-Stokes equations, Comput. Math. Appl., 26 (1993), pp. 33-38.
14. W. LAYTON AND P. RABIER, An element-by-element parallel, low order element for the Stokes problem, ICMA Report 92-173, Institute for Computational Mathematics and Applications, Univ. of Pittsburgh, 1992.
15. W. LENFERINK, An accurate solution procedure for fluid flow with natural convection, Department of Mathematics, Catholic University of Nijmegen, the Netherlands, 1993.
16. M. M. STANISIC', The Mathematical Theory of Turbulence, Springer-Verlag, New York, 1980.
17. R. TEMAM, Navier-Stokes equations and nonlinear functional analysis, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 41, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1983.
18. J. XU, Two grid finite element discretization techniques for linear and nonlinear PDE, SIAM J. Numer. Anal., 33 (1996), to appear.
19. X. YE AND C. A. HALL, The construction of a null basis for the discrete divergence operator, J. Comput. Appl. Math., 58 (1995), pp. 117-133.
20. O. PIRONNEAU, Finite Element Methods for Fluids, John Wiley, New York, 1990.
21. W. J. LAYTON AND H. W. J. LENFERINK, Two-level, Picard defect correction for the Navier-Stokes equations at high Reynolds number, Appl. Math. Comput., 80 (1995), pp. 1-12.
22. O. DOROK, G. LUBE, U. RISCH, F. SCHIEWECK, AND L. TOBISKA, Finite Element Discretization of the Navier-Stokes Equations, Preprint 15/92, "Otto von Guericke" University, Magdeburg, 1992.
23. E. L. ALLGOWER, K. BÖHMER, F. A. POTRA AND W. C. RHEINBOLDT, A mesh-independence principle for operator equations and their discretizations, SIAM J. Numer. Anal., 23 (1986), pp. 160-169.