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Convergence results for the vector penalty-projection and two-step artificial compressibility methods
1. | Aix-Marseille Université, Laboratoire d’Analyse, Topologie, Probabilités - CNRS UMR7353, Centre de Mathématiques et Informatique, 13453 Marseille cedex 13, France |
2. | Université de Bordeaux & IPB, Institut Mathématiques de Bordeaux - CNRS UMR5251, ENSEIRB-MATMECA, Talence, France |
References:
[1] |
Ph. Angot, J.-P. Caltagirone and P. Fabrie, Vector penalty-projection method for the solution of unsteady incompressible flows, in "Finite Volumes for Complex Applications V'' (eds. R. Eymard and J.-M. Hérard), ISTE, London, (2008), 169-176. |
[2] |
Ph. Angot, J.-P. Caltagirone and P. Fabrie, A spectacular vector penalty-projection method for Darcy and Navier-Stokes problems, in "Finite Volumes for Complex Applications VI'' (eds J. Fořt, et al.), International Symposium FVCA6 in Prague, June 6-10, Springer Proceedings in Mathematics, 4, Vol. 1, Springer-Verlag, Berlin, (2011), 39-47. |
[3] |
Ph. Angot, J.-P. Caltagirone and P. Fabrie, A new fast method to compute saddle-points in constrained optimization and applications, Applied Mathematics Letters, 25 (2012), 245-251.
doi: 10.1016/j.aml.2011.08.015. |
[4] |
Ph. Angot, J.-P. Caltagirone and P. Fabrie, A fast vector penalty-projection method for in-compressible non-homogeneous or multiphase Navier-stokes problems, Applied Mathematics Letters, 2012, in press.
doi: 10.1016/j.aml.2012.01.037. |
[5] |
F. Boyer and P. Fabrie, "Éléments d'Analyse pour l'Étude de quelques Modèles d'Écoulements de Fluides Visqueux Incompressibles," Mathématiques & Applications, 52, Springer-Verlag, 2006. |
[6] |
A. J. Chorin, A numerical method for solving incompressible viscous flow problems, J. Comput. Phys., 2 (1967), 12-26.
doi: 10.1016/0021-9991(67)90037-X. |
[7] |
A. J. Chorin, Numerical solution of the Navier-Stokes equations, Math. Comput., 22 (1968), 745-762.
doi: 10.1090/S0025-5718-1968-0242392-2. |
[8] |
C. Foias and R. Temam, Remarques sur les équations de Navier-Stokes stationnaires et les phénomènes successifs de bifurcation, Annali della Scuolo Normale Superiore di Pisa, Classe di Scienze (4), 5 (1978), 28-63. |
[9] |
V. Girault and P.-A. Raviart, "Finite Element Methods for the Navier-Stokes Equations. Theory and Algorithms," Springer Series in Comput. Math., 5, Springer-Verlag, Berlin, 1986. |
[10] |
J.-L. Guermond, P. D. Minev and J. Shen, An overview of projection methods for incompressible flows, Comput. Meth. Appl. Mech. Engrg., 195 (2006), 6011-6045.
doi: 10.1016/j.cma.2005.10.010. |
[11] |
O. A. Ladyzhenskaya, "The Mathematical Theory of Viscous Incompressible Flow," 2nd edition, Mathematics and its Applications, Vol. 2 , Gordon and Breach, Science Publishers, New York-London-Paris, 1969. |
[12] |
J. Leray, Essai sur les mouvements plans d'un liquide visqueux que limitent des parois, J. Math. Pures Appl., 13 (1934), 331-418. |
[13] |
J.-L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires," Dunod & Gauthier-Villars, Paris, 1969. |
[14] |
J. Shen, On error estimates of the penalty method for unsteady Navier-Stokes equations, SIAM J. Numer. Anal., 32 (1995), 386-403.
doi: 10.1137/0732016. |
[15] |
J. Shen, On a new pseudocompressibility method for the incompressible Navier-Stokes equations, Appl. Numer. Math., 21 (1996), 71-90.
doi: 10.1016/0168-9274(95)00132-8. |
[16] |
J. Simon, Compact sets in the space $L^p(0,T;B)$, Ann. Mat. Pura Appl. (4), 146 (1987), 65-96. |
[17] |
R. Temam, Une méthode d'approximation de la solution des équations de Navier-Stokes, Bull. Soc. Math. France, 96 (1968), 115-152. |
[18] |
R. Temam, Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires. I, Arch. Ration. Mech. Anal., 32 (1969), 135-153. |
[19] |
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), 377-385. |
[20] |
R. Temam, "Navier-Stokes Equations. Theory and Numerical Analysis," 3rd edition, Studies in Mathematics and its Applications, 2, North-Holland Publishing Co., Amsterdam, 1984. |
show all references
References:
[1] |
Ph. Angot, J.-P. Caltagirone and P. Fabrie, Vector penalty-projection method for the solution of unsteady incompressible flows, in "Finite Volumes for Complex Applications V'' (eds. R. Eymard and J.-M. Hérard), ISTE, London, (2008), 169-176. |
[2] |
Ph. Angot, J.-P. Caltagirone and P. Fabrie, A spectacular vector penalty-projection method for Darcy and Navier-Stokes problems, in "Finite Volumes for Complex Applications VI'' (eds J. Fořt, et al.), International Symposium FVCA6 in Prague, June 6-10, Springer Proceedings in Mathematics, 4, Vol. 1, Springer-Verlag, Berlin, (2011), 39-47. |
[3] |
Ph. Angot, J.-P. Caltagirone and P. Fabrie, A new fast method to compute saddle-points in constrained optimization and applications, Applied Mathematics Letters, 25 (2012), 245-251.
doi: 10.1016/j.aml.2011.08.015. |
[4] |
Ph. Angot, J.-P. Caltagirone and P. Fabrie, A fast vector penalty-projection method for in-compressible non-homogeneous or multiphase Navier-stokes problems, Applied Mathematics Letters, 2012, in press.
doi: 10.1016/j.aml.2012.01.037. |
[5] |
F. Boyer and P. Fabrie, "Éléments d'Analyse pour l'Étude de quelques Modèles d'Écoulements de Fluides Visqueux Incompressibles," Mathématiques & Applications, 52, Springer-Verlag, 2006. |
[6] |
A. J. Chorin, A numerical method for solving incompressible viscous flow problems, J. Comput. Phys., 2 (1967), 12-26.
doi: 10.1016/0021-9991(67)90037-X. |
[7] |
A. J. Chorin, Numerical solution of the Navier-Stokes equations, Math. Comput., 22 (1968), 745-762.
doi: 10.1090/S0025-5718-1968-0242392-2. |
[8] |
C. Foias and R. Temam, Remarques sur les équations de Navier-Stokes stationnaires et les phénomènes successifs de bifurcation, Annali della Scuolo Normale Superiore di Pisa, Classe di Scienze (4), 5 (1978), 28-63. |
[9] |
V. Girault and P.-A. Raviart, "Finite Element Methods for the Navier-Stokes Equations. Theory and Algorithms," Springer Series in Comput. Math., 5, Springer-Verlag, Berlin, 1986. |
[10] |
J.-L. Guermond, P. D. Minev and J. Shen, An overview of projection methods for incompressible flows, Comput. Meth. Appl. Mech. Engrg., 195 (2006), 6011-6045.
doi: 10.1016/j.cma.2005.10.010. |
[11] |
O. A. Ladyzhenskaya, "The Mathematical Theory of Viscous Incompressible Flow," 2nd edition, Mathematics and its Applications, Vol. 2 , Gordon and Breach, Science Publishers, New York-London-Paris, 1969. |
[12] |
J. Leray, Essai sur les mouvements plans d'un liquide visqueux que limitent des parois, J. Math. Pures Appl., 13 (1934), 331-418. |
[13] |
J.-L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires," Dunod & Gauthier-Villars, Paris, 1969. |
[14] |
J. Shen, On error estimates of the penalty method for unsteady Navier-Stokes equations, SIAM J. Numer. Anal., 32 (1995), 386-403.
doi: 10.1137/0732016. |
[15] |
J. Shen, On a new pseudocompressibility method for the incompressible Navier-Stokes equations, Appl. Numer. Math., 21 (1996), 71-90.
doi: 10.1016/0168-9274(95)00132-8. |
[16] |
J. Simon, Compact sets in the space $L^p(0,T;B)$, Ann. Mat. Pura Appl. (4), 146 (1987), 65-96. |
[17] |
R. Temam, Une méthode d'approximation de la solution des équations de Navier-Stokes, Bull. Soc. Math. France, 96 (1968), 115-152. |
[18] |
R. Temam, Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires. I, Arch. Ration. Mech. Anal., 32 (1969), 135-153. |
[19] |
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), 377-385. |
[20] |
R. Temam, "Navier-Stokes Equations. Theory and Numerical Analysis," 3rd edition, Studies in Mathematics and its Applications, 2, North-Holland Publishing Co., Amsterdam, 1984. |
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