Spectral element discretization of the circular driven cavity. Part IV: The Navier-Stokes equations

Journal of Mathematical Fluid Mechanics

Volumn 6, Issue 2, 2004, Pages 121-156

  Belhachmi, Zakaria ^a   Bernardi, Christine ^b   Karageorghis, Andreas ^c  

^a UNIVERSITÉ DE LORRAINE   (France)

^b UNIVERSITY OF CYPRUS   (Cyprus)

^c UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

Author keywords

Driven cavity; Navier Stokes equations; Spectral elements

Indexed keywords

APPROXIMATION THEORY; ERROR ANALYSIS; GALERKIN METHODS; LAGRANGE MULTIPLIERS; NONLINEAR SYSTEMS;

DRIVEN CAPACITY; SOBOLEV SPACES; SPECTRAL ELEMENTS;

NAVIER STOKES EQUATIONS;

EID: 4544355519     PISSN: 14226928     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00021-003-0101-7     Document Type: Article

References (12)

1. Z. BELHACHMI, C. BERNARDI AND A. KARAGEORGHIS, Spectral element discretization of the circular driven cavity. Part II: The bilaplacian equation, SIAM J. Numer. Anal. 38 (2001), 1926-1960.
2. Z. BELHACHMI, C. BERNARDI AND A. KARAGEORGHIS, Spectral Element Discretization of the Circular Driven Cavity. Part III: The Stokes Equations in Primitive Variables, J. math. Fluid Mech. 5 (2003), 24-69.
3. F. BEN BELGACEM, The Mortar finite element method with Lagrange multipliers, Numer. Math. 84 (1999), 173-197.
4. C. BERNARDI, C. CANUTO AND Y. MADAY, Generalized inf-sup condition for Chebyshev spectral approximation of the Stokes problem, SIAM J. Numer. Anal. 25 (1988), 1237-1271.
5. C. BERNARDI, M. DAUGE, Y. MADAY AND M. AZAÏEZ, Spectral Methods for Axisymmetric Domains, Series in Applied Mathematics 3, Gauthier-Villars & North-Holland, 1999.
6. C. BERNARDI AND A. KARAGEORGHIS, Spectral element discretization of the circular driven cavity. Part I: The Laplace equation, SIAM J. Numer. Anal. 36 (1999), 1435-1465.
7. C. BERNARDI AND Y. MADAY, Spectral Methods, in: Handbook of Numerical Analysis V, P. G. Ciariet and J.-L. Lions (eds.), 1997, 209-485.
8. C. BERNARDI, Y. MADAY AND A. T. PATERA, Domain decomposition by the mortar element method, in: Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters, H. G. Kaper and M. Garbey (eds.), N.A.T.O. ASI Series C 384, 1993, 269-286.
9. F. BREZZI, J. RAPPAZ AND P.-A. RAVIART, Finite dimensional approximation of nonlinear problems, Part I: Branches of nonsingular solutions, Numer. Math. 36 (1980), 1-25.
10. V. GIRAULT AND P.-A. RAVIART, Finite Element Methods for the Navier-Stokes Equations, Theory and Algorithms, Springer-Verlag, Heidelberg, 1986.
11. R. A. NICOLAIDES, Existence, uniqueness and approximation for generalized saddle point problems, SIAM J. Numer. Anal. 19 (1982), 349-357.
12. D. SERRE, Équations de Navier-Stokes stationnaires avec données peu régulières, Ann. Scuola Norm. Sup. Pisa, Cl. Sci. Serie IV, 10 (1983), 543-559.