Analysis of a stabilized finite element approximation of the Oseen equations using orthogonal subscales

Applied Numerical Mathematics

Volumn 58, Issue 3, 2008, Pages 264-283

  Codina, Ramon ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Convection dominated flows; inf sup condition; Orthogonal subscales; Stabilized finite element methods

Indexed keywords

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; GALERKIN METHODS; PROBLEM SOLVING;

CONVECTION-DOMINATED FLOWS; INF-SUP CONDITION; ORTHOGONAL SUBSCALES; STABILIZED FINITE ELEMENT METHODS;

FINITE ELEMENT METHOD;

EID: 38549097236     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2006.11.011     Document Type: Article

References (30)

1. Ainsworth M., and Oden J.T. A Posteriori Error Estimation in Finite Element Analysis (2000), Wiley-Interscience, New York
2. Becker R., and Braack M. A finite element pressure gradient stabilization for the Stokes equations based on local projections. Calcolo 38 (2001) 173-199
3. Blasco J., and Codina R. Space and time error estimates for a first order, pressure stabilized finite element method for the incompressible Navier-Stokes equations. Applied Numerical Mathematics 38 (2001) 475-497
4. Bochev P., Cai Z., Manteuffel T.A., and McCormick S.F. Analysis of velocity-flux first-order system least-squares principles for the Navier-Stokes equations: Part I. SIAM Journal on Numerical Analysis 35 (1998) 990-1009
5. Brenner S.C., and Scott L.R. The Mathematical Theory of Finite Element Methods (1994), Springer, Berlin
6. Brezzi F., and Douglas J. Stabilized mixed methods for the Stokes problem. Numerische Mathematik 53 (1988) 225-235
7. Brezzi F., and Fortin M. Mixed and Hybrid Finite Element Methods (1991), Springer, Berlin
8. Brezzi F., and Fortin M. A minimal stabilisation procedure for mixed finite element methods. Numerische Mathematik 89 (2001) 457-491
9. Brezzi F., Franca L.P., Hughes T.J.R., and Russo A. b = ∫ g. Computer Methods in Applied Mechanics and Engineering 145 (1997) 329-339
10. Brezzi F., and Pitkäranta J. On the stabilization of finite element approximation of the Stokes problem. In: Hackbush W. (Ed). Efficient Solution of Elliptic Systems (1984), Vieweg, Braunschweig 11-19
11. Brezzi F., Rappaz J., and Raviart P.A. Finite dimensional approximation of nonlinear problems. Part I: Branches of non-singular solutions. Numerische Mathematik 36 (1981) 1-25
12. Brooks A.N., and Hughes T.J.R. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equation. Computer Methods in Applied Mechanics and Engineering 32 (1982) 199-259
13. Burman E., and Hansbo P. Edge stabilization for Galerkin approximations of convection-diffusion-reaction problems. Computer Methods in Applied Mechanics and Engineering 193 (2004) 1437-1453
14. Chacón T. A term by term stabilization algorithm for the finite element solution of incompressible flow problems. Numerische Mathematik 79 (1998) 283-319
15. Codina R. Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods. Computer Methods in Applied Mechanics and Engineering 190 (2000) 1579-1599
16. Codina R. A stabilized finite element method for generalized stationary incompressible flows. Computer Methods in Applied Mechanics and Engineering 190 (2001) 2681-2706
17. Codina R. Stabilized finite element approximation of transient incompressible flows using orthogonal subscales. Computer Methods in Applied Mechanics and Engineering 191 (2002) 4295-4321
18. Codina R., and Blasco J. A finite element formulation for the Stokes problem allowing equal velocity-pressure interpolation. Computer Methods in Applied Mechanics and Engineering 143 (1997) 373-391
19. Codina R., and Blasco J. Analysis of a pressure-stabilized finite element approximation of the stationary Navier-Stokes equations. Numerische Mathematik 87 (2000) 59-81
20. Douglas J., and Wang J. An absolutely stabilized finite element method for the Stokes problem. Mathematics of Computation 52 (1989) 495-508
21. Franca L., Hughes T.J.R., Loula A.F.D., and Miranda I. A new family of stable elements for nearly incompressible elasticity based on a mixed Petrov-Galerkin finite element formulation. Numerische Mathematik 53 (1988) 123-141
22. Franca L., and Stenberg R. Error analysis of some Galerkin least-squares methods for the elasticity equations. SIAM Journal on Numerical Analysis 28 (1991) 1680-1697
23. Franca L.P., and Frey S.L. Stabilized finite element methods: II. The incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 99 (1992) 209-233
24. Girault V., and Raviart P.A. Finite Element Methods for Navier-Stokes Equations (1986), Springer, Berlin
25. Gresho P.M. On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part I: Theory. International Journal for Numerical Methods in Fluids 11 (1990) 587-620
26. Hughes T.J.R. Multiscale phenomena: Green's function, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized formulations. Computer Methods in Applied Mechanics and Engineering 127 (1995) 387-401
27. Hughes T.J.R., Feijóo G.R., Mazzei L., and Quincy J.B. The variational multiscale method-a paradigm for computational mechanics. Computer Methods in Applied Mechanics and Engineering 166 (1998) 3-24
28. Hughes T.J.R., Franca L.P., and Balestra M. A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuška-Brezzi condition: a stable Petrov-Galerkin formulation for the Stokes problem accommodating equal-order interpolations. Computer Methods in Applied Mechanics and Engineering 59 (1986) 85-99
29. Tobiska L., and Lube G. A modified streamline-diffusion method for solving the stationary Navier-Stokes equations. Numerische Mathematik 59 (1991) 13-29
30. Tobiska L., and Verfürth R. Analysis of a streamline diffusion finite element method for the Stokes and Navier-Stokes equations. SIAM Journal on Numerical Analysis 33 (1996) 107-127