Free access
Issue
ESAIM: M2AN
Volume 39, Number 6, November-December 2005
Page(s) 1115 - 1147
DOI http://dx.doi.org/10.1051/m2an:2005048
Published online 15 November 2005
  1. R.A. Adams, Sobolev Spaces. Academic Press, New York (1975).
  2. A.S. Almgren, J.B. Bell, P. Colella, L.H. Howell and M.L. Welcome, A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations. Technical Report LNBL-39075, UC-405 (1996).
  3. C.E. Baumann and J.T. Oden, A discontinuous hp finite element method for convection-diffusion problems. Comput. Methods Appl. Mech. Engrg. 175 (1999) 311–341. [CrossRef] [MathSciNet]
  4. J. Blasco and R. Codina, Error estimates for an operator-splitting method for incompressible flows. Appl. Numer. Math. 51 (2004) 1–17. [CrossRef] [MathSciNet]
  5. J. Blasco, R. Codina and A. Huerta, A fractional-step method for the incompressible Navier-Stokes equations related to a predictor-multicorrector algorithm. Int. J. Numer. Meth. Fl. 28 (1997) 1391–1419. [CrossRef]
  6. P.G. Ciarlet, The finite element methods for elliptic problems. North-Holland, Amsterdam (1978).
  7. A.J. Chorin, Numerical solution of the Navier-Stokes equations. Math. Comp. 22 (1968) 745–762. [CrossRef] [MathSciNet]
  8. M. Crouzeix and P.A. Raviart, Conforming and non conforming finite element methods for solving the stationary Stokes equations. RAIRO Anal. Numér. R3 (1973) 33–76.
  9. C. Dawson and J .Proft, Discontinuous and coupled continuous/discontinuous Galerkin methods for the shallow water equations. Comput. Methods Appl. Mech. Engrg. 191 (2002) 4721–4746. [CrossRef] [MathSciNet]
  10. C. Dawson, S. Sun and M. Wheeler, Compatible algorithms for coupled flow and transport. Comput. Methods Appl. Mech. Engrg. (2003) 2565–2580.
  11. E. Fernandez-Cara and M.M. Beltram, The convergence of two numerical schemes for the Navier-Stokes equations. Numer. Math. 55 (1989) 33–60. [CrossRef] [MathSciNet]
  12. V. Girault and J.-L. Lions, Two-grid finite-element schemes for the steady Navier-Stokes problem in polyhedra. Portugal. Math. 58 (2001) 25–57.
  13. V. Girault and P.A. Raviart, Finite element methods for Navier-Stokes equations. Lecture Notes in Math. 749, Springer-Verlag, Berlin, Heidelberg, New-York (1979).
  14. V. Girault, B. Rivière and M.F. Wheeler, A discontinuous Galerkin method with non-overlapping domain decomposition for the Stokes and Navier-Stokes problems. Math. Comp. 74 (2005) 53–84. [CrossRef] [MathSciNet]
  15. R. Glowinski, Finite element methods for Incompressible Viscous Flows, in Numerical Methods for Fluids (Part 3), Handbook of Numerical Analysis, 9, Elsevier, North-Holland (2003).
  16. P. Grisvard, Elliptic problems in nonsmooth domains, Pitman Monogr. Studies Pure Appl. Math. 24, Pitman, Boston, MA (1985).
  17. J.L. Guermond and L. Quartapelle, On the approximation of the unsteady Navier-Stokes equations by finite element projection methods. Numer. Math. 80 (1998) 207–238. [CrossRef] [MathSciNet]
  18. J.L. Guermond and J. Shen, Velocity-correction projection methods for incompressible flows. SIAM J. Numer. Anal. 41 (2003) 112–134. [CrossRef] [MathSciNet]
  19. J.L. Guermond and J. Shen, A new class of truly consistent splitting schemes for incompressible flows. J. Comput. Phys. 192 (2003) 262–276. [CrossRef] [MathSciNet]
  20. S. Kaya and B. Rivière, A discontinuous subgrid eddy viscosity method for the time-dependent Navier-Stokes equations. SIAM J. Numer. Anal. (2005), to appear.
  21. P. Lesaint and P.A. Raviart, On a finite element method for solving the neutron transport equation, in Mathematical Aspects of Finite Element Methods in Partial Differential Equations, C.A. de Boor Ed., Academic Press (1974) 89–123.
  22. J.-L. Lions and E. Magenes, Problèmes aux Limites non Homogènes et Applications, I. Dunod, Paris (1968).
  23. J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Paris (1969).
  24. A. Quarteroni, F. Saleri and A. Veneziani, Factorization methods for the numerical approximation of Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 188 (2000) 505–526. [CrossRef] [MathSciNet]
  25. R. Rannacher, On Chorin's projection method for the incompressible Navier-Stokes equations, Navier-Stokes equations: Theory and Numerical Methods, R. Rautmann et al. Eds., Springer (1992).
  26. B. Rivière, M.F. Wheeler and V. Girault, Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Part I. Comput. Geosci. 3 (1999) 337–360. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  27. R. Temam, Sur l'approximation de la solution des equations de Navier-Stokes par la méthode des pas fractionnaires (I), (II). Arch. Rational Mech. Anal. 33 (1969) 377–385. [CrossRef] [MathSciNet]
  28. R. Temam, Navier-Stokes equations. Theory and numerical analysis. North-Holland, Amsterdam (1979).
  29. S. Turek, On discrete projection methods for the incompressible Navier-Stokes equations: an algorithmic approach. Comput. Methods Appl. Mech. Engrg. 143 (1997) 271–288. [CrossRef] [MathSciNet]
  30. M.F. Wheeler, An elliptic collocation-finite element method with interior penalties. SIAM J. Numer. Anal. 15 (1978) 152–161. [CrossRef] [MathSciNet]
  31. N.N. Yanenko, The method of fractional steps. The solution of problems of mathematical physics in several variables. Springer-Verlag, New York (1971).

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