Approximation of Burgers' equation by pseudo-spectral methods
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 16 (1982) no. 4, p. 375-404
@article{M2AN_1982__16_4_375_0,
     author = {Maday, Y. and Quateroni, A.},
     title = {Approximation of Burgers' equation by pseudo-spectral methods},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {16},
     number = {4},
     year = {1982},
     pages = {375-404},
     zbl = {0514.65084},
     mrnumber = {684831},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1982__16_4_375_0}
}
Maday, Y.; Quateroni, A. Approximation of Burgers' equation by pseudo-spectral methods. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 16 (1982) no. 4, pp. 375-404. http://www.numdam.org/item/M2AN_1982__16_4_375_0/

[1] R A Adams, Sobolev spaces, Academic Press, New York (1975) | MR 450957 | Zbl 0314.46030

[2] J Babuska, A K Aziz, " Survey lectures on the mathematical foundations of the finite element method ", in The Mathematical Foundations of The Finite Element Method with Applications to Partial Differential Equations, Ed Aziz, Academic Press, NewYork (1972), 3-343 | Zbl 0268.65052

[3] J Bergh, J Lofstrom, Interpolation Spaces An Introduction, Springer Verlag, Berlin (1976) | MR 482275 | Zbl 0344.46071

[4] F Brezzi, J Rappaz, P A Raviart, Finite dimensional approximation of nonlinear problems Part I branches of nonsingular solutions Num Math , 36 (1980), 1-25 | MR 595803 | Zbl 0488.65021

[5] C Canuto, A Quarteroni, Spectral and pseudo-spectral methods for parabolic problems with non periodic boundary conditions, Calcolo, 18 (1981), pp 197-217 | MR 647825 | Zbl 0485.65078

[6] C Canuto, A Quarteroni Approximation results for orthogonal polynomials in Sobolev spaces, Math Comput, 38 (1982), pp 67 86 | MR 637287 | Zbl 0567.41008

[7] A Davis, P Rabinowitz Methods of Numerical Integration, Academic Press,New York (1975) | MR 448814 | Zbl 0304.65016

[8] D Gottlieb, S A Orszag, Numerical Analysis of Spectral Methods Theory and Applications, Regional Conference Series in applied mathematics, SIAM, Philadelphia (1977) | MR 520152 | Zbl 0412.65058

[9] H O Kreiss, J Oliger, Stability of the Fourier method, SIAM J Num An ,16, 3 (1949), 421-433 | MR 530479 | Zbl 0419.65076

[10] J L Lions, E Magenes, Non Homogeneous Boundary Value Problems and Applications, Springer Verlag, Berlin (1972) | Zbl 0223.35039

[11] Y Maday, A Quarteroni Legendre and Chebyshev spectral approximation of Burgers equation, Numer Math, 37 (1981), pp 321-332 | Zbl 0452.41007

[12] Y Maday, A Quarteroni, Spectral and pseudo-spectral approximations of Navier-Stokes equations, SIAM J Numer Anal, 19 (1982), pp 769-780 | Zbl 0503.76035

[13] R E Nickell, D K Gartling, G Strang, Spectral decomposition in advection-diffusion analysis by finite element methods, Comp Meths Appl Mech Eng 17/18 (1979), 561-580 | Zbl 0403.76072

[14] G Szego, Orthogonal Polynomials, AMS Colloquium publications, vol 23,AMS, New York (1939) | JFM 65.0278.03 | Zbl 0023.21505