|
Stabilized finite element method for Navier-Stokes equations with physical boundary conditions
Author(s):
M.
Amara;
D.
Capatina-Papaghiuc;
D.
Trujillo.
Journal:
Math. Comp.
76
(2007),
1195-1217.
MSC (2000):
Primary 35Q30, 65N12;
Secondary 65N30
Posted:
March 15, 2007
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
This paper deals with the numerical approximation of the 2D and 3D Navier-Stokes equations, satisfying nonstandard boundary conditions. This lays on the finite element discretisation of the corresponding Stokes problem, which is achieved through a three-fields stabilized mixed formulation. A priori and a posteriori error bounds are established for the nonlinear problem, ascertaining the convergence of the method. Finally, numerical tests are presented, including mesh refinement via error indicators.
References:
-
- 1.
- Amara, M. and Bernardi, C., Convergence of a finite element discretization of the Navier-Stokes equations in vorticity and stream function formulation, Mathematical Modelling and Numerical Analysis, vol. 33, n. 5, p. 1033-1056 (1999) MR 1726723 (2000k:65200)
- 2.
- Amara, M., Capatina-Papaghiuc, D., Trujillo, D.: Stabilized method for the Navier-Stokes equations with nonstandard boundary conditions, Preprint LMA UPPA, n. 0325, p. 1- 29 (2003) (http://lma.univ-pau.fr/publis/publis_pre.php)
- 3.
- Amara, M., Capatina-Papaghiuc, D., Trujillo, D.: A 3D numerical model for the vorticity-velocity-pressure formulation of the Navier-Stokes problem, Preprint LMA UPPA, n. 0510, p.1-11 (2005) (http://lma.univ-pau.fr/publis/publis_pre.php)
- 4.
- Amara, M., Chacon Vera, E. and Trujillo, D.: Vorticity-velocity-pressure formulation for Stokes problem, Math. of Comp., vol. 73, n. 248, p. 1673-1697 (2004) MR 2059731 (2005d:65201)
- 5.
- Bernardi, C. and Girault, V.: A local regularization operator for triangular and quadrilateral finite elements, SIAM J. Numer. Anal., vol. 35, n. 5, p. 1893-1916 (1998) MR 1639966 (99g:65107)
- 6.
- Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York (1991) MR 1115205 (92d:65187)
- 7.
- Brezzi, F., Rappaz, J., Raviart, P.-A.: Finite Dimensional Approximation of Nonlinear Problems. Branches of Nonsingular Solutions, Numer. Math., vol. 36, 1-25 (1980) MR 595803 (83f:65089a)
- 8.
- Caloz, G., Rappaz, J.: Numerical Analysis for Nonlinear and Bifurcation Problems, Handbook of Numerical Analysis, vol. V, P.G. Ciarlet and J.L. Lions eds, North-Holland, Amsterdam (1997) MR 1470227
- 9.
- Ciarlet, P.: The Finite Element Method for Elliptic Problems, North-Holland (1978) MR 0520174 (58:25001)
- 10.
- Conca, C., Pares, C., Pironneau, O. and Thiriet, M.: Navier-Stokes Equations with imposed pressure and velocity fluxes, International Journal for Numerical Methods in Fluids, vol. 20, 267-287 (1995) MR 1316046 (96d:76019)
- 11.
- Costabel, M.: A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains, Mathematical Methods in the Applied Sciences, vol. 12, 365-368 (1990) MR 1048563 (91c:35028)
- 12.
- Dubois, F., Salaün, M., Salmon, S.: Vorticity-velocity-pressure and stream function-vorticity formulations for the Stokes problem, J. Math. Pures Appl., vol. 82, p. 1395-1451 (2003) MR 2020806 (2004i:35247)
- 13.
- Girault, V. and Raviart, P.-A.: Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms, Springer-Verlag (1986) MR 851383 (88b:65129)
- 14.
- Grisvard, P.: Elliptic Problems in Nonsmooth Domains, Pitman (1985) MR 775683 (86m:35044)
- 15.
- Pousin, J., Rappaz, J.: Consistency, stability, a priori and a posteriori errors for Petrov-Galerkin methods applied to nonlinear problems, Numer. Math. 69, 213-231 (1994) MR 1310318 (95k:65111)
Similar Articles:
Retrieve articles in Mathematics of Computation
with MSC
(2000):
35Q30, 65N12,
65N30
Retrieve articles in all Journals with MSC
(2000):
35Q30, 65N12,
65N30
Additional Information:
M.
Amara
Affiliation:
Laboratoire de Mathématiques Appliquées-CNRS UMR5142, Université de Pau et des Pays de l'Adour, BP 1155, 64013 PAU CEDEX
Email:
mohamed.amara@univ-pau.fr
D.
Capatina-Papaghiuc
Affiliation:
Laboratoire de Mathématiques Appliquées-CNRS UMR5142, Université de Pau et des Pays de l'Adour, BP 1155, 64013 PAU CEDEX
Email:
daniela.capatina@univ-pau.dr
D.
Trujillo
Affiliation:
Laboratoire de Mathématiques Appliquées-CNRS UMR5142, Université de Pau et des Pays de l'Adour, BP 1155, 64013 PAU CEDEX
Email:
david.trujillo@univ-pau.fr
DOI:
10.1090/S0025-5718-07-01929-1
PII:
S 0025-5718(07)01929-1
Received by editor(s):
June 4, 2004
Received by editor(s) in revised form:
July 6, 2005
Posted:
March 15, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org