×

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
PDFBibTeX XMLCite
Full Text: DOI

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 · doi:10.1090/S0025-5718-1982-0637287-3
[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 · doi:10.3792/pja/1195518266
[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 · doi:10.1007/BF01666742
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.