Prediction-correction Legendre spectral scheme for incompressible fluid flow

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1. [1] J.L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires. Dunod, Paris (1969). Zbl0189.40603MR259693
2. [2] R. Temam, Navier-Stokes Equations. North-Holland, Amsterdam (1977). Zbl0383.35057MR769654
3. [3] P.J. Roach, Computational Fluid Dynamics, 2nd edition. Hermosa Publishers, Albuquerque (1976). MR411358
4. [4] Guo Ben-yu, Finite Difference Methods for Partial Differential Equations. Science Press, Beijing (1988). 
5. [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. [6] V. Girault and P. Raviart, Finite Element Approximation of the Navier-Stokes Equations, Lecture Note in Math. 794. Springer-Verlag, Berlin (1979). Zbl0413.65081MR548867
7. [7] D. Gottlieb and S.A. Orszag, Numerical Analysis of Spectral Methods, CBMS-NSF Reginal Conference Series in Applied Mathematics 26. SIAM, Philadelphia (1977). Zbl0412.65058MR520152
8. [8] C. Canuto, M.Y. Hussaini, A Quarteroni and T. A. Zang, Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin (1988). Zbl0658.76001MR917480
9. [9] A.J. Chorin, Numerical methods of thermal convection. J. Comp. Phys 2 (1976) 12-26. 
10. [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. Zbl0241.65080MR261180
11. [11] Kuo Ben-yu, Numerical methods for incompressible viscous flow. Scientia Sinica 20 (1977) 287-304. Zbl0367.76044MR502906
12. [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. [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. Zbl0644.76025
14. [14] C. Bernardi, G. Coppoletta and Y. Maday, Some spectral approximations of two-dimemsional fourth-order problems. Math. Comp. 59 (1992) 63-76. Zbl0754.65088MR1134714
15. [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. Zbl0811.65097MR1298626
16. [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. MR1426977
17. [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. Zbl0909.76067MR1618444
18. [18] R.A. Adams, Sobolev Space. Academic Press, New York (1975). Zbl0314.46030MR450957
19. [19] J.L. Lions and E. Magenes, Problèmes aux Limites Non homogènes et applications, Vol. 1. Dunod, Paris (1968). Zbl0165.10801MR247243
20. [20] C. Canuto and A. Quarteroni, Approximation results for orthogonal polynomials in Sobolev space. Math. Comp. 38 (1982) 67-68. Zbl0567.41008MR637287
21. [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.