Mixed Laguerre-Legendre pseudospectral method for incompressible fluid flow in an infinite strip
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- by Ben-yu Guo and Cheng-long Xu PDF
- Math. Comp. 73 (2004), 95-125 Request permission
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
- Robert A. Adams, Sobolev spaces, Pure and Applied Mathematics, Vol. 65, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0450957
- 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.
- C. Bernardi and Y. Maday, Basic Results on Spectral Methods, R94022, Univ. Pierre et Marie Curie, Paris, 1994.
- 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.
- John P. Boyd, Spectral methods using rational basis functions on an infinite interval, J. Comput. Phys. 69 (1987), no. 1, 112–142. MR 892255, DOI 10.1016/0021-9991(87)90158-6
- 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.
- Philip J. Davis and Philip Rabinowitz, Methods of numerical integration, 2nd ed., Computer Science and Applied Mathematics, Academic Press, Inc., Orlando, FL, 1984. MR 760629
- Daniele Funaro and Otared Kavian, Approximation of some diffusion evolution equations in unbounded domains by Hermite functions, Math. Comp. 57 (1991), no. 196, 597–619. MR 1094949, DOI 10.1090/S0025-5718-1991-1094949-X
- Ben-Yu Guo, Error estimation of Hermite spectral method for nonlinear partial differential equations, Math. Comp. 68 (1999), no. 227, 1067–1078. MR 1627789, DOI 10.1090/S0025-5718-99-01059-5
- Ben-Yu Guo and Li-Ping He, The fully discrete Legendre spectral approximation of two-dimensional unsteady incompressible fluid flow in stream function form, SIAM J. Numer. Anal. 35 (1998), no. 1, 146–176. MR 1618444, DOI 10.1137/S0036142996297084
- S. Losinsky, Sur le procédé d’interpolation de Fejér, C. R. (Doklady) Acad. Sci. URSS (N.S.) 24 (1939), 318–321 (French). MR 0002001
- Ben-Yu Guo and Cheng-Long Xu, Hermite pseudospectral method for nonlinear partial differential equations, M2AN Math. Model. Numer. Anal. 34 (2000), no. 4, 859–872. MR 1784489, DOI 10.1051/m2an:2000100
- Ben-yu Guo and Cheng-long Xu, On two-dimensional unsteady incompressible fluid flow in an infinite strip, Math. Methods Appl. Sci. 23 (2000), no. 18, 1617–1636. MR 1797937, DOI 10.1002/1099-1476(200012)23:18<1617::AID-MMA176>3.0.CO;2-9
- Jae Ryong Kweon and R. Bruce Kellogg, Smooth solution of the compressible Navier-Stokes equations in an unbounded domain with inflow boundary condition, J. Math. Anal. Appl. 220 (1998), no. 2, 657–675. MR 1614936, DOI 10.1006/jmaa.1997.5872
- J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris; Gauthier-Villars, Paris, 1969 (French). MR 0259693
- J.-L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications. Vol. I, Die Grundlehren der mathematischen Wissenschaften, Band 181, Springer-Verlag, New York-Heidelberg, 1972. Translated from the French by P. Kenneth. MR 0350177
- Y. Maday, B. Pernaud-Thomas, and H. Vandeven, Reappraisal of Laguerre type spectral methods, Rech. Aérospat. 6 (1985), 353–375 (French, with English summary); English transl., Rech. Aérospat. (English Edition) 6 (1985), 13–35. MR 850680
- G. Mastroianni and G. Monegato, Nyström interpolants based on zeros of Laguerre polynomials for some Wiener-Hopf equations, IMA J. Numer. Anal. 17 (1997), no. 4, 621–642. MR 1476342, DOI 10.1093/imanum/17.4.621
- Gabor Szegö, Orthogonal polynomials, American Mathematical Society Colloquium Publications, Vol. 23, American Mathematical Society, Providence, R.I., 1959. Revised ed. MR 0106295
- Roger Temam, Navier-Stokes equations. Theory and numerical analysis, Studies in Mathematics and its Applications, Vol. 2, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. MR 0609732
- Xu Cheng-long and Guo Ben-yu, Laguerre pseudospectral method for nonlinear partial differential equations, J. Comp. Math., 20 (2002), 413–428.
- 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.
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
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Math. Comp. 73 (2004), 95-125
- MSC (2000): Primary 65M70, 41A30, 35Q30
- DOI: https://doi.org/10.1090/S0025-5718-03-01521-7
- MathSciNet review: 2034112