Spectral-Finite Element Method for Compressible Fluid Flow

Guo Ben-yu; Cao Wei-ming

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1992 > 13(8): 677-692

Guo Ben-yu, Cao Wei-ming. Spectral-Finite Element Method for Compressible Fluid Flow[J]. Applied Mathematics and Mechanics, 1992, 13(8): 677-692.

Citation:

Guo Ben-yu, Cao Wei-ming. Spectral-Finite Element Method for Compressible Fluid Flow[J]. Applied Mathematics and Mechanics, 1992, 13(8): 677-692.

Citation:

Guo Ben-yu, Cao Wei-ming. Spectral-Finite Element Method for Compressible Fluid Flow[J]. Applied Mathematics and Mechanics, 1992, 13(8): 677-692.

PDF( 907 KB)

Spectral-Finite Element Method for Compressible Fluid Flow

Shanghai University of Science and Technology, Shanghai

Received Date: 1991-04-15
Publish Date: 1992-08-15

Abstract

Abstract

In this paper, a combined Fourier spectral-finite element method is proposed for solving n-dimensional (n=2,3), semi-periodic compressible fluid flow problems. The strict error estimation as well as the convergence rate, is presented.
- compressible fluid flow,
- spectral method,
- finite element method,
- error estimation

FullText(HTML)

References(17)

References

[1]	Roache, P. J., Computational Fluid Dynamics, 2nd Ed, Hermosa Publishers, Albuqueque (1976).
[2]	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.
[3]	郭本瑜,《偏微分方程的差分方法》,科学出版社(1988).
[4]	Kuo Pen-yu, Résolution numérique de fluidè compressible, C. R. Acad. Sc. Paris, 291A(1980), 167-171.
[5]	Guo Ben-yu, Strict error estimation of numerical solution of compressible flow in two-dimensional space, Scientia Sinica, 26A(1983), 482-498.
[6]	Chung, T. J., Finite Element Analysis in Fluid Dynamics, McGraw-Hill International Book Company (1978).
[7]	Guo Ben-yu and Ma He-ping, Strict error estimation for a spectral method of compressible fluid flow, CalColo, 24 (1987), 263-282.
[8]	Canuto, C., Y. Maday and A. Quarteroni, Analysis of the combined finite element and Fourier interpolation, Numer. Math., 39(1982), 205-220.
[9]	Canuto, C., Y. Maday and A. Quarteroni, Combined finite element and spectral approximation of the Navier-Stokes equations, Numer. Math., 44(1984), 201-217.
[10]	Guo Ben-yu, Spectral-difference method for solving two-dimensional vorticity equations, J.Comput. Math., 6(1988), 238-257.
[11]	Guo Ben-yu and Cao Wei-ming, Spectral-finite element method for solving two-dimensional vorticity equations, Acta Mathematicae Applicatae Sinica, 7(1991), 257-271.
[12]	Guo Ben-yu and Cao Wei-ming, Spectral-finite element method for solving three-dimensional vorticity equations, J. Greek Math. Soc., 32(1990), 258-280.
[13]	Guo Ben-yu and Cao Wei-ming, Spectral-finite element method for solving two-dimensional Navier-Stokes equation(1988). (unpublished).
[14]	Adams, R. A., Sobolev Spaces, Academic Press, New York(1975).
[15]	Grisvard, P., Equations differentielles abstraites, Ann. Sci. Ecole Norm. Sup., 4(1969),311-395.
[16]	Ciarlet, P. G., The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam (1978).
[17]	Schatz, A., V. Thomee and L. B. Wahlbin, Maximum norm stability and error estimates in parabolic finite element equations, Commun. Pure Appl. Math., 33(1980), 265-304.