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Strict error estimation for a spectral method of compressible fluid flow. (English) Zbl 0668.76072

A Fourier spectral method for compressible flow in n-dimensional space with periodic boundary conditions is constructed. We give a strict error estimation, from which the convergence follows with some assumptions.

MSC:

76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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References:

[1] R. D. Richtmyer, K. W. Morton,Difference method for initial value problem, Interscience, New York, 1967. · Zbl 0155.47502
[2] P. J. Roach,Computational fluid dynamics, Hermosa publisher, 1976
[3] Kuo Pen-Yu,Résolution numérique de fluide compressible, C. R. Acad. Sci. Paris, 291A (1980), 167–171. · Zbl 0446.76062
[4] Guo Ben-yu,Strict error estimation of numerical solution of compressible flow in two-dimensional space, Sci. Sinica, 26A (1983), 482–498. · Zbl 0517.76075
[5] C. Canuto, A. Quarteroni,Approximation results for orthogonal polynomials in Sobolev spaces, Math. Comp., 38 (1982), 67–86. · Zbl 0567.41008
[6] Gyo Ben-yu,Spectral method for solving Navier-Stokes equations, Sci. Sinica, 28 (1985), 1139–1153. · Zbl 0626.76034
[7] Atusi, Tani,The existence and uniqueness of the solution of equations describing compressible viscous fluid flow in a domain, Proc. Japan Acad., 52 (1976), 334–337. · Zbl 0364.35039
[8] Guo Ben-yu,The convergence of spectral scheme for solving two-dimensional vorticity equation, J. C. M., 1, (1983), 353–362. · Zbl 0599.76030
[9] Guo Ben-yu,Error estimation of spectral method for solving three-dimensional vorticity equation, Acta Math. Appl. Sinica, 2, (1985), 229–240. · Zbl 0626.76024
[10] Griffiths D.,The stability of finite difference approximations to nonlinear partial differential equations, Bulletin of IMA, 18, (1982), December, 210–215. · Zbl 0515.73080
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