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Legendre and Chebyshev spectral approximations of Burgers’ equation. (English) Zbl 0452.41007


MSC:

41A10 Approximation by polynomials
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A25 Rate of convergence, degree of approximation
65N15 Error bounds for boundary value problems involving PDEs
35A25 Other special methods applied to PDEs
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References:

[1] Adams, R.A.: Sobolev spaces. New York-San Francisco-London: Academic Press 1975 · Zbl 0314.46030
[2] Babuska, I., Szabo, B.A., Katz, I.N.: TheP-version of the finite element method. Report of the Washington University (St. Louis), 1979
[3] Bergh, J., Löfstrom, J.: Interpolation spaces. An introduction. Berlin-Heidelberg-New York: Springer 1976
[4] Brezzi, F., Rappaz, J., Raviart, P.A.: Finite dimensional approximation of nonlinear problems. Part I: branches of non singular solution, Numer. Math.36, 1-25 (1980) · Zbl 0488.65021
[5] Canuto, C., Quarteroni, A.: Proprietés d’approximation dans les espaces de Sobolev de systèmes de polynômes orthogonaux. C.R. Acad Sc. Paris,290, A-928 (1980) · Zbl 0508.65052
[6] Canuto, C., Quarteroni, A.: Approximation results for orthogonal polynomials in Sobolev spaces. Math. Comput (in press 1981) · Zbl 0508.65053
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[8] Grisvard, P.: Espaces intermédiaires entre espaces de Sobolev avec poids. Ann. Scuola Norm. Sup. Pisa17, 255-296 (1963) · Zbl 0117.08602
[9] Lions, J.L.: Quelques méthodes de résolution des problèmes aux limites non linéaires. Paris: Dunod 1969
[10] Lions, J.L., Magenes, E.: Non homogeneous boundary value problems and applications, Berlin-Heidelberg-New York: Springer 1972 · Zbl 0227.35001
[11] Maday, Y., Quarteroni, A.: Spectral and pseudo-spectral approximations of Navier-Stokes equations SIAM J. Numer. Anal (in press, 1981) · Zbl 0452.41007
[12] Maday, Y., Quarteroni, A.: Approximation of Burger’s equation by pseudo-spectral methods Math. Comput (in press, 1981) · Zbl 0452.41007
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