Error analysis of pressure-correction schemes for the time-dependent stokes equations with open boundary conditions

SIAM Journal on Numerical Analysis

Volumn 43, Issue 1, 2005, Pages 239-258

  Guermond, J L ^a   Minev, P ^b   Shen, J ^c  

^a CNRS   (France)

^b UNIVERSITY OF ALBERTA   (Canada)

^c PURDUE UNIVERSITY   (United States)

Author keywords

Finite elements; Incompressibility; Navier Stokes and Stokes equations; Open boundary conditions; Pressure correction methods; Spectral approximations

Indexed keywords

INCOMPRESSIBILITY; NAVIER-STOKES AND STOKES EQUATIONS; OPEN BOUNDARY CONDITIONS; PRESSURE-CORRECTION METHODS; SPECTRAL APPROXIMATIONS;

APPROXIMATION THEORY; BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; NAVIER STOKES EQUATIONS; PRESSURE EFFECTS;

ERROR ANALYSIS;

EID: 33644595768     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/040604418     Document Type: Article

References (27)

1. S. C. BRENNER AND R. L. SCOTT, The Mathematical Theory of Finite Element Methods, Texts Appl. Math. 15, Springer, New York, 1994.
2. A. J. CHORIN, On the convergence of discrete approximations to the Navier-Stokes equations, Math. Comp., 23 (1969), pp. 341-353.
3. W. E AND J.-G. LIU, Projection method. I. Convergence and numerical boundary layers, SIAM J. Numer. Anal., 32 (1995), pp. 1017-1057.
4. P. M. GRESHO AND S. T. CHAN, On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via finite element method that also introduces a nearly consistent mass matrix. Part I, Internat. J. Numer. Methods Fluids, 11 (1990), pp. 587-620.
5. P. M. GRESHO AND S. T. CHAN, On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via finite element method that also introduces a nearly consistent mass matrix. Part II, Internat. J. Numer. Methods Fluids, 11 (1990), pp. 621-659.
6. J.-L. GUERMOND, Some practical implementations of projection methods for Navier-Stokes equations, RAIRO Model. Math. Anal. Numer., 30 (1996), pp. 637-667.
7. Also in C. R. Acad. Sci. Paris Sér. I Math., 319 (1994), pp. 887-892.
8. J.-L. GUERMOND, Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier-Stokes par une technique de projection incrémentale, M2AN Math. Model. Numer. Anal., 33 (1999), pp. 169-189.
9. Also in C. R. Acad. Sci. Paris Sér. I Math., 325 (1997), pp. 1329-1332.
10. J.-L. GUERMOND AND L. QUARTAPELLE, On the approximation of the unsteady Navier-Stokes equations by finite element projection methods, Numer. Math., 80 (1998), pp. 207-238.
11. J. L. GUERMOND AND J. SHEN, Velocity-correction projection methods for incompressible flows, SIAM J. Numer. Anal., 41 (2003), pp. 112-134.
12. J.-L. GUERMOND AND J. SHEN, On the error estimates for the rotational pressure-correction projection methods, Math. Comp., 73 (2004), pp. 1719-1737.
13. J. L. GUERMOND AND J. SHEN, Quelques résultats nouveaux sur les méthodes de projection, C. R. Acad. Sci. Paris Sér. I Math., 333 (2001), pp. 1111-1116.
14. J. L. GUERMOND, P. MINEV, AND J. SHEN, An overview of projection methods for incompressible flows, Comput. Methods Appl. Mech. Engrg., to appear.
15. M. J. LEE, B. D. OH, AND Y. B. KIM, Canonical fractional-step methods and consistent boundary conditions for the incompressible Navier-Stokes equations, J. Comput. Phys., 168 (2001), pp. 73-100.
16. M. ORLT AND A.-M. SÄNDIG, Regularity of viscous Navier-Stokes flows in nonsmooth domains, in Boundary Value Problems and Integral Equations in Nonsmooth Domains (Luminy, 1993), S. Nicaise, M. Costabel, and M. Dauge, eds., Lecture Notes in Pure and Appl. Math. 167, Marcel Dekker, New York, 1995, pp. 185-201.
17. J. B. PEROT, An analysis of the fractional step method, J. Comput. Phys., 108 (1993), pp. 51-58.
18. A. QUARTERONI, F. SALERI, AND A. VENEZIANI, Analysis of the Yosida method for the incompressible Navier-Stokes equations, J. Math. Pures Appl. (9), 78 (1999), pp. 473-503.
19. A. QUARTERONI, F. SALERI, AND A. VENEZIANI, Factorization methods for the numerical approximation of Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 188 (2000), pp. 505-526.
20. R. RANNACHER, On Chorin's projection method for the incompressible Navier-Stokes equations, in The Navier-Stokes Equations II - Theory and Numerical Methods (Oberwolfach, 1991), Lecture Notes in Math. 1530, Springer, Berlin, 1992, pp. 167-183.
21. J. SHEN, Efficient spectral-Galerkin method. I. Direct solvers of second- and fourth-order equations using Legendre polynomials, SIAM J. Sci. Comput., 15 (1994), pp. 1489-1505.
22. J. SHEN, A new pseudo-compressibility method for the Navier-Stokes equations, Appl. Numer. Math., 21 (1996), pp. 71-90.
23. J. SHEN, On error estimates of projection methods for the Navier-Stokes equations: Second-order schemes, Math. Comp., 65 (1996), pp. 1039-1065.
24. R. TEMAM, Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires II, Arch. Ration. Mech. Anal., 33 (1969), pp. 377-385.
25. R. TEMAM, Navier-Stokes Equations: Theory and Numerical Analysis, North-Holland, Amsterdam, 1984.
26. L. J. P. TIMMERMANS, P. D. MINEV, AND F. N. VAN DE VOSSE, An approximate projection scheme for incompressible flow using spectral elements, Internat. J. Numer. Methods Fluids, 22 (1996), pp. 673-688.
27. J. VAN KAN, A second-order accurate pressure-correction scheme for viscous incompressible flow, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 870-891.