Prediction-correction Legendre spectral scheme for incompressible fluid flow
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 33 (1999) no. 1, p. 113-120
@article{M2AN_1999__33_1_113_0,
     author = {Li-Ping, He and De-Kang, Mao and Ben-Yu, Guo},
     title = {Prediction-correction Legendre spectral scheme for incompressible fluid flow},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {33},
     number = {1},
     year = {1999},
     pages = {113-120},
     zbl = {0917.76062},
     mrnumber = {1685747},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1999__33_1_113_0}
}
Li-Ping, He; De-Kang, Mao; Ben-Yu, Guo. Prediction-correction Legendre spectral scheme for incompressible fluid flow. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 33 (1999) no. 1, pp. 113-120. http://www.numdam.org/item/M2AN_1999__33_1_113_0/

[1] J.L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires. Dunod, Paris (1969). | MR 259693 | Zbl 0189.40603

[2] R. Temam, Navier-Stokes Equations. North-Holland, Amsterdam (1977). | MR 769654 | Zbl 0383.35057

[3] P.J. Roach, Computational Fluid Dynamics, 2nd edition. Hermosa Publishers, Albuquerque (1976). | MR 411358

[4] Guo Ben-Yu, Finite Difference Methods for Partial Differential Equations. Science Press, Beijing (1988).

[5] J.T. Oden, R.H. Zienkiewicz, R.H. Gallagher and C. Talor, Finite Element Methods in Flow Problems. John Willey, New York (1974).

[6] V. Girault and P. Raviart, Finite Element Approximation of the Navier-Stokes Equations, Lecture Note in Math. 794. Springer-Verlag, Berlin (1979). | MR 548867 | Zbl 0413.65081

[7] D. Gottlieb and S.A. Orszag, Numerical Analysis of Spectral Methods, CBMS-NSF Reginal Conference Series in Applied Mathematics 26. SIAM, Philadelphia (1977). | MR 520152 | Zbl 0412.65058

[8] C. Canuto, M.Y. Hussaini, A Quarteroni and T. A. Zang, Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin (1988). | MR 917480 | Zbl 0658.76001

[9] A.J. Chorin, Numerical methods of thermal convection. J. Comp. Phys 2 (1976) 12-26.

[10] J.L. Lions, On the numerical approximation of some equations arising in hydrodynamics. In Numerical Solution of Fluid Problems in Continuum Physics, SIAM-AMS Proceedings II, G. Birkhoff and R.S. Varga, Eds. AMS, Providence (1970) 11-23. | MR 261180 | Zbl 0241.65080

[11] Kuo Ben-Yu, Numerical methods for incompressible viscous flow. Scientia Sinica 20 (1977) 287-304. | MR 502906 | Zbl 0367.76044

[12] Jie Shen, On pressure stabilization method and projection method for unsteady Navier-Stokes equations. In Advance in Computer Methods for Partial Differential Equations VII, R. Vichnevetsky, D. Knight and G. Richter, Eds. IMACS, New Brunswick (1992) 658-602.

[13] P.M. Gresho and R.L. Sani, On pressure boundary conditions for incompressible Navier-Stokes equations. Int. J. Numer. Meth. Fluids 7 (1987) 1111-1145. | Zbl 0644.76025

[14] C. Bernardi, G. Coppoletta and Y. Maday, Some spectral approximations of two-dimemsional fourth-order problems. Math. Comp. 59 (1992) 63-76. | MR 1134714 | Zbl 0754.65088

[15] Jie Shen, Efficient Spectral-Galerkin method I, Direct solvers of second and fourth order equations using Legendre polynomials. SIAM Sci. Comput. 15 (1994) 1489-1505. | MR 1298626 | Zbl 0811.65097

[16] Guo Ben-Yu, He Li-Ping and Mao De-Kang, On two-dimensional Navier-Stokes equation in stream fonction form. J. Math. Anal. Appl. 205 (1997) 1. | MR 1426977

[17] Guo Ben-Yu and He Li-Ping, The fully discrete Legendre spectral approximation of two-dimensional unsteady incompressible fluid flow in stream function form. SIAM J. Numer. Anal. 35 (1998) 146. | MR 1618444 | Zbl 0909.76067

[18] R.A. Adams, Sobolev Space. Academic Press, New York (1975). | MR 450957 | Zbl 0314.46030

[19] J.L. Lions and E. Magenes, Problèmes aux Limites Non homogènes et applications, Vol. 1. Dunod, Paris (1968). | MR 247243 | Zbl 0165.10801

[20] C. Canuto and A. Quarteroni, Approximation results for orthogonal polynomials in Sobolev space. Math. Comp. 38 (1982) 67-68. | MR 637287 | Zbl 0567.41008

[21] He Li-Ping, Mao De-Kang and Guo Ben-Yu, A prediction-correction Legendre spectral scheme for two-dimensional unsteady incompressible fluid flow in stream function form, RR 1996-3, Department of Mathematics, Shanghai University.