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Analysis of the combined finite element and Fourier interpolation. (English) Zbl 0496.42002


MSC:

42A15 Trigonometric interpolation
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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References:

[1] Adams, R.A.: Sobolev Spaces. Academic Press: New York-San Francisco-London 1975 · Zbl 0314.46030
[2] Bramble, J.H., Hilbert, S.R.: Bounds for a class of linear functionals with applications to Hermite interpolation. Numer. Math.16, 362-369 (1971) · Zbl 0214.41405
[3] Canuto, C., Fujii, H., Quarteroni, A.: Approximation of symmetry breaking bifurcations for the Rayleigh convection problem, to appear · Zbl 0534.76089
[4] Canuto, C., Quarteroni, A.: Approximation results for orthogonal polynomials in Sobolev spaces. Math. Comput.38, 67-86 (1982) · Zbl 0567.41008
[5] Ciarlet, P.G.: The finite element method for elliptic problems. North-Holland: Amsterdam 1978 · Zbl 0383.65058
[6] Dupont, T., Scott, R.: Polynomial approximation of functions in sobolev spaces. Math. Comput.34, 441-464 (1980) · Zbl 0423.65009
[7] Gottlieb, D., Orszag, S.A.: Numerical analysis of spectral methods: Theory and applications. CMBS Regional Conference Series in Applied Mathematics26, SIAM, Philadelphia 1977 · Zbl 0412.65058
[8] Grisvard, P.: Equations diff?rentielles abstraites. Ann. Sci. Ecole Norm. Sup.4, 311-395 (1969) · Zbl 0193.43502
[9] Kreiss, H.O., Oliger, J.: Stability of the Fourier method. SIAM J. Num Anal.16, 421-433 (1979) · Zbl 0419.65076
[10] Lions, J.L., Magenes, E.: Non homogeneous boundary value problems and applications. Springer: Berlin-Heidelberg-New York 1972 · Zbl 0227.35001
[11] Maday, Y.: Sur quelques propri?t?s des approximations par des m?thodes spectrales dans les espaces de Sobolev ? poids. Applications ? la r?solution de probl?mes non lin?aires. Th?se de troisi?me cycle. Universit? de Paris VI (1981)
[12] Pasciak, J.E.: Spectral and pseudo-spectral methods for advection equations. Math. Comput.35, 1081-1092 (1980) · Zbl 0448.65071
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