On the error estimates for the rotational pressure-correction projection methods

Mathematics of Computation

Volumn 73, Issue 248, 2004, Pages 1719-1737

  Guermond, J L ^a   Shen, Jie ^b  

^a CNRS   (France)

^b PURDUE UNIVERSITY   (United States)

Author keywords

Finite elements; Fractional step methods; Incompressibility; Navier Stokes equations; Projection methods; Spectral approximations

Indexed keywords

EID: 5644272882     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-03-01621-1     Document Type: Article

References (20)

1. David L. Brown, Ricardo Cortez, and Michael L. Minion. Accurate projection methods for the incompressible Navier-Stokes equations. J. Comput. Phys., 168(2):464-499, 2001. MR 2002a:76112
2. A. J. Chorin. Numerical solution of the Navier-Stokes equations. Math. Comp., 22:745-762, 1968. MR 39:3723
3. A. J. Chorin. On the convergence of discrete approximations to the Navier-Stokes equations. Math. Comp., 23:341-353, 1969. MR 39:3724
4. W. E and J.G. Liu. Projection method I: Convergence and numerical boundary layers. SIAM J. Numer. Anal., 32:1017-1057, 1995. MR 96e:65061
5. W. E and J.G. Liu. Projection method. III. Spatial discretization on the staggered grid. Math. Comp., 71(237):27-47, 2002. MR 2002k:65155
6. K. Goda. A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows. J. Comput. Phys., 30:76-95, 1979.
7. J.-L. Guermond. Un résultat de convergence à l'ordre deux en temps pour l'approximation des équations de Navier-Stokes par une technique de projection. Modél. Math. Anal. Numér. (M2AN), 33(1):169-189, 1999. MR 2000k:65171
8. J.L. Guermond and Jie Shen. Velocity-correction projection methods for incompressible flows. To appear in SIAM J. Numer. Anal.
9. G. E. Karniadakis, M. Israeli, and S. A. Orszag. High-order splitting methods for the incompressible Navier-Stokes equations. J. Comput. Phys., 97:414-443, 1991. MR 92h:76066
10. S. A. Orszag, M. Israeli, and M. Deville. Boundary conditions for incompressible flows. J. Sci. Comput., 1:75-111, 1986.
11. R. Rannacher. On Chorin's projection method for the incompressible Navier-Stokes equations. Lecture Notes in Mathematics, vol. 1530, 1991. MR 95a:65149
12. Jie Shen. On error estimates of the projection methods for the Navier-Stokes equations: first-order schemes. SIAM J. Numer. Anal., 29:57-77, 1992. MR 92m:35213
13. Jie Shen. On pressure stabilization method and projection method for unsteady Navier-Stokes equations. In R. Vichnevetsky, D. Knight, and G. Richter, editors, Advances in Computer Methods for Partial Differential Equations, pages 658-662, IMACS, 1992.
14. Jie Shen. Efficient spectral-Galerkin method I. direct solvers for second- and fourth-order equations by using Legendre polynomials. SIAM J. Sci. Comput., 15:1489-1505, 1994. MR 95j:65150
15. Jie Shen. On error estimates of projection methods for the Navier-Stokes equations: second-order schemes. Math. Comp, 65:1039-1065, July 1996. MR 96j:65091
16. J. C. Strikwerda and Y. S. Lee. The accuracy of the fractional step method. SIAM J. Numer. Anal., 37(1):37-47, 1999. MR 2000h:65127
17. R. Temam. Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires ii. Arch. Rat. Mech. Anal., 33:377-385, 1969. MR 39:5968
18. R. Temam. Navier-Stokes Equations: Theory and Numerical Analysis. North-Holland, Amsterdam, 1984. MR 58:29439
19. L. J. P. Timmermans, P. D. Minev, and F. N. Van De Vosse. An approximate projection scheme for incompressible flow using spectral elements. Int. J. Numer. Methods Fluids, 22:673-688, 1996.
20. J. van Kan. A second-order accurate pressure-correction scheme for viscous incompressible flow. SIAM J. Sci. Stat. Comput., 7:870-891, 1986. MR 87h:76008