Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Mixed Laguerre-Legendre pseudospectral method for incompressible fluid flow in an infinite strip


Authors: Ben-yu Guo and Cheng-long Xu
Journal: Math. Comp. 73 (2004), 95-125
MSC (2000): Primary 65M70, 41A30, 35Q30
DOI: https://doi.org/10.1090/S0025-5718-03-01521-7
Published electronically: June 19, 2003
MathSciNet review: 2034112
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we investigate the mixed Laguerre-Legendre interpolation approximation and its application. Some approximation results are established. A mixed Laguerre-Legendre pseudospectral scheme is constructed for incompressible fluid flow in an infinite strip. Its stability and convergence are proved. Numerical results show the efficiency of this new approach.


References [Enhancements On Off] (What's this?)

  • 1. R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975. MR 56:9247
  • 2. C. Bernardi, G. Coppoletta and Y. Maday, Some spectral approximations of multi-dimensional fourth-order problems, Internal Report 90021, Laboratoire $d^{'}$Analyse Numérique, Université Pierre et Marie Curie, Paris, 1990.
  • 3. C. Bernardi and Y. Maday, Basic Results on Spectral Methods, R94022, Univ. Pierre et Marie Curie, Paris, 1994.
  • 4. C. Bernardi and Y. Maday, Spectral methods, in Handbook of Numerical Analysis, 209-486, ed. by P. G. Ciarlet and J. L. Lions, Elsevier, Amsterdam, 1997.
  • 5. J. P. Boyd, Spectral methods using rational basis function in an infinite interval, J. Comp. Phys., 69(1987), 112-142. MR 88e:65093
  • 6. O. Coulaud, D. Funaro and O.Kavian, Laguerre spectral approximation of elliptic problems in exterior domains, Comp. Mech. in Appl. Mech and Engi., 80 (1990), 451-458.
  • 7. P.J. Davis and P. Rabinowitz, Methods of Numerical Integration, Academic Press, New York, 1984. MR 86d:65004
  • 8. D. Funaro and O. Kavian, Approximation of some diffusion evolution equations in unbounded domains by Hermite functions, Math. Comp., 57(1990), 597-619. MR 92k:35156
  • 9. Guo Ben-yu, Error estimation for Hermite spectral method for nonlinear partial differential equations, Math. Comp., 68(1999), 1067-1078. MR 99i:65111
  • 10. Guo Ben-yu and He Li-ping, The fully discrete Legendre spectral approximation of two-dimensional unsteady incompressible fluid flow in steam function form, SIAM J. Numer. Anal., 35(1998), 146-176. MR 99f:76103
  • 11. Guo Ben-yu and Jie Shen, Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval, Numer. Math., 86(2000), 635-654. MR 2001:65152
  • 12. Guo Ben-yu and Xu Cheng-long, Hermite pseudospectral method for nonlinear partial differential equations, RAIRO Math. Model and Numer. Anal., 34(2000), 859-872. MR 2001f:65142
  • 13. Guo Ben-yu and Xu Cheng-long, On two-dimensional unsteady incompressible fluid flow in an infinity strip, Math. Meth. in Appl. Sci., 23(2000), 1617-1636. MR 2001j:76030
  • 14. J. R. Kweon and R. B. Kellogg, Smooth solution of the compressible Navier-Stokes equations in an unbounded domain with inflow boundary condition, J. Math. Anal. Appl., 220(1998), 657-675. MR 99b:35169
  • 15. J. L. Lions, Quèlques méthodes de Résolution des Problèms aux Limités Non Linéaires, Dunod, Paris, 1969. MR 41:4326
  • 16. J. L. Lions and E. Magenes, Nonhomogeneous boundary value problems and applications, Vol I, Dunod, Paris, 1972. MR 50:2670
  • 17. Y. Maday, B. Pernaud-Thomas and H. Vandeven, One réhabilitation des méthods spèctrales de type Laguerre, Rech. A$\acute{e}$rospat., 6(1985), 353-379. MR 88b:65135
  • 18. G. Mastroianni and G. Monegato, Nyström interpolants based on zeros of Laguerre polynomials for some Weiner-Hopf equations, IMA J. of Numer. Anal., 17(1997), 621-642. MR 98j:45011
  • 19. G.Szegö, Orthogonal Polynomials, Amer. Math, Soc., New York, 1959. MR 21:5029
  • 20. R. Temam, Navier-Stokes Equation, North-Holland, Amsterdam, 1977. MR 58:29439
  • 21. Xu Cheng-long and Guo Ben-yu, Laguerre pseudospectral method for nonlinear partial differential equations, J. Comp. Math., 20 (2002), 413-428.
  • 22. Xu Cheng-long and Guo Ben-yu, Mixed Laguerre-Legendre spectral method for incompressible fluid flow in an infinite strip, Advances in Comp. Math., 16(2002), 77-96.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 65M70, 41A30, 35Q30

Retrieve articles in all journals with MSC (2000): 65M70, 41A30, 35Q30


Additional Information

Ben-yu Guo
Affiliation: Shanghai E-Institute for Scientific Computation, Department of Mathematics, Shanghai Normal University, Shanghai, 200234, Peoples Republic of China

Cheng-long Xu
Affiliation: Department of Applied Mathematics, Tongji University, Shanghai, 200092, Peoples Republic of China

DOI: https://doi.org/10.1090/S0025-5718-03-01521-7
Keywords: Incompressible fluid flow, infinite strip, Laguerre-Legendre pseudospectral method
Received by editor(s): August 16, 2001
Received by editor(s) in revised form: April 12, 2002
Published electronically: June 19, 2003
Additional Notes: The work of the first author is partially supported by The Special Founds for Major State Basic Research Projects of China G1999032804 and The Shanghai Natural Science Foundation N.00JC14057
Article copyright: © Copyright 2003 American Mathematical Society

American Mathematical Society