| [1] |
Girault V，Raviart P A.Finite Element Approximation of the Navier-Stokes Equations[M].Lecture Notes in Mathematics.794.Berlin: Springer-Verlag,1979.
|
| [2] |
GUO Ben-yu. Difference method for fluid dynamics-numerical solution of primitive equations[J].Scientia Sinica,Series A,1981,24(3):297-312.
|
| [3] |
郭本瑜.偏微分方程的差分方法[M].北京：科学出版社，1988.
|
| [4] |
Roache P J.Computational Fluid Dynamics[M].2nd Ed. Albuquerque:Hermosa Publishers,1976.
|
| [5] |
Téman R.Navier-Stokes Equations[M].Amsterdam: North-Holland,1977.
|
| [6] |
Bernardi C, Maday Y.Spectral methods[A].In:Ciarlet P G,Lions J L,Eds.Handbook of Numerical Analysis.Vol 5.Techniques of Scientific Computing[C].Amsterdam:Elsevier,1997,209-486.
|
| [7] |
Boyd J P.Chebyshev and Fourier Spectral Methods[M].Berlin:Springer-Verlag,1989.
|
| [8] |
Canuto C, Hussaini M Y,Quarteroni A,et al.Spectral Methods in Fluid Dynamics[M].Berlin:Springer-Verlag,1988.
|
| [9] |
Funaro P.Polynomial Approximations of Differential Equations[M].Berlin:Springer-Verlag,1992.
|
| [10] |
Gottlieb D, Orszag S A.Numerical Analysis of Spectral Methods: Theory and Applications[M].Philadelphia: SIAM-CBMS, 1977.
|
| [11] |
GUO Ben-yu.Spectral Methods and Their Applications[M].Singapore:World Scientific,1998.
|
| [12] |
GUO Ben-yu. Spectral method for Navier-Stokes equations[J].Scientia Sinica, Series A,1985,28(11):1139-1153.
|
| [13] |
GUO Ben-yu, MA He-ping. Combined finite element and pseudospectral method for the two-dimensional evolutionary Navier-Stokes equations[J].SIAM J Numer Anal,1993,30(4):1066-1083. doi: 10.1137/0730055
|
| [14] |
Hald O H. Convergence of Fourier methods for Navier-Stokes equations[J].J Comput Phys,1981,40(2):305-317. doi: 10.1016/0021-9991(81)90212-6
|
| [15] |
Maday Y, Quarteroni A. Spectral and pseudospectral approximations of the Navier-Stokes equations[J].SIAM J Numer Anal,1982,19(4):761-780. doi: 10.1137/0719053
|
| [16] |
MA He-ping, GUO Ben-yu. Combined finite element and pseudospectral method for the three-dimensional Navier-Stokes equations[J].Chinese Annals of Mathematics,Series B,1992,13(3):350-367.
|
| [17] |
Boyd J P. The choice of spectral functions on a sphere for boundary and eigenvalue problems: a comparison of Chebyshev, Fourier and associated Legendre expansion[J].Mon Weather Rev,1978,106(8):1184-1191. doi: 10.1175/1520-0493(1978)106<1184:TCOSFO>2.0.CO;2
|
| [18] |
Efstathiou G. A model of supernova feedback in galaxy formation[J].Mon Not R Astron Soc,2000,317(3):697-719. doi: 10.1046/j.1365-8711.2000.03665.x
|
| [19] |
Haltiner G J, Williams R T.Numerical Prediction and Dynamical Meteorology[M].New York: John Wiley & Sons, 1980.
|
| [20] |
Williamson D L, Drake J B, Hack J J,et al.A standard test set for numerical approximations to the shallow water equations in spherical geometry[J].J Comput Phys,1992,102(1):211-224. doi: 10.1016/S0021-9991(05)80016-6
|
| [21] |
Bramble J H, Pasciak J E.A boundary parametric approximation to linearized scalar potential magnetostatic field problem[J].Appl Numer Math,1985,1(6):493-514. doi: 10.1016/0168-9274(85)90034-0
|
| [22] |
CAO Wei-ming, GUO Ben-yu. A pseudospectral method for vorticity equations on spherical surface[J].Acta Math Appl Sinica,1997,13(2):176-187. doi: 10.1007/BF02015139
|
| [23] |
GUO Ben-yu. A spectral method for the vorticity equation on the surface[J].Math Comp,1995,64(211):1067-1079.
|
| [24] |
GUO Ben-yu, CAO Wei-ming. A spectral method for the fluid flow with low Mach number on the spherical surface[J].SIAM J Numer Anal,1995,32(6):1764-1777. doi: 10.1137/0732080
|
| [25] |
GUO Ben-yu. Jacobi approximations in certain Hilbert spaces and their applications to singular differential equations[J].J Math Anal Appl,2000,243(2):373-408.
|
| [26] |
GUO Ben-yu, HUANG Wei.Mixed Jacobi-spherical harmonic spectral method for Navier-Stokes equations[J].Appl Numer Math,2007,57(8):939-961. doi: 10.1016/j.apnum.2006.09.003
|
| [27] |
GUO Ben-yu, WANG Li-lian.Jacobi interpolation approximations and their applications to singular differential equations[J].Adv in Comput Math,2001,14(3):227-276. doi: 10.1023/A:1016681018268
|
| [28] |
GUO Ben-yu, WANG Li-lian. Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces[J].J Approx Theory,2004,128(1):1-41. doi: 10.1016/j.jat.2004.03.008
|
| [29] |
Chorin A J. The numerical solution of the Navier-Stokes equations for an incompressible fluid[J].Bull Amer Math Soc,1967,73(6):928-931. doi: 10.1090/S0002-9904-1967-11853-6
|
| [30] |
Chorin A J. Numerical solution of the Navier-Stokes equations[J].Math Comp,1968,22(104):745-762. doi: 10.1090/S0025-5718-1968-0242392-2
|
| [31] |
Lions J L. On the numerical approximation of some equations arising in hydrodynamics[A].In:Birkhoff G, Varga R S, Eds.Numerical Solution of Field Problems in Continuum Physics, SIAM-AMS Proceedings Ⅱ[C].Providence, Rhode Island:AMS,1970,11-23.
|
| [32] |
Courant R, Hilbert D.Methods of Mathematical Physics[M].Vol 1.New York: Interscience Publisher, 1953.
|
| [33] |
Bergh J, Lfstrm J.Interpolation Spaces,an Introduction[M].Berlin: Springer-Verlag,1976.
|
| [34] |
Dumas G, Leonard A.A divergence-free spectral expansions method for three-dimensional flow in spherical-gap geometries[J].J Comput Phys,1994,111(2):205-219. doi: 10.1006/jcph.1994.1056
|
| [35] |
Friedman A.Partial Differential Equations[M].New York: Holt, Rinehart and Winston, 1969.
|
| [36] |
Adams R A.Sobolev Spaces[M].New York: Academic Press, 1975.
|
| [37] |
陈恕行.偏微分方程概论[M].北京:人民教育出版社,1981.
|
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