A new efficient spectral Galerkin method for singular perturbation problems

Journal of Scientific Computing

Volumn 11, Issue 4, 1996, Pages 411-437

  Liu, W B ^a   Shen, Jie ^b  

^a UNIVERSITY OF KENT   (United Kingdom)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Boundary layer; Convection diffusion; Singular perturbation; Spectral Galerkin method

Indexed keywords

BOUNDARY LAYERS; ERROR ANALYSIS; INTEGRAL EQUATIONS; NUMERICAL METHODS; PERTURBATION TECHNIQUES; PROBLEM SOLVING; SPECTRUM ANALYSIS;

CONVECTION DIFFUSION EQUATION; SINGULAR PERTURBATION PROBLEMS; SPECTRAL GALERKIN METHOD;

BOUNDARY VALUE PROBLEMS;

EID: 0030386328     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02088955     Document Type: Article

References (20)

1. Ascher, U. M., Christiansen, J., and Russell, R. D. (1994). A collocation solver for mixed order systems of boundary problems. Math. Comp. 33, 659-679.
2. Ascher, U., Mattheij R. M., and Russell, R. (1988). Numerical Solution of Boundary Value Problems for Ordinary Differential Equation, Prentice-Hall, New Jersey.
3. Canuto, C. (1988). Spectral methods and a maximum principle. Math. Comp. 51, 615-629.
4. Canute, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A. (1988). Spectral methods in fluid dynamics, Series of Computational Physics, Springer-Verlag.
5. Eisen, H., and Heinrichs, W. (1992). A new method of stabilization for singular perturbation problems with spectral methods. SIAM J. Numer. Anal. 29, 107-122.
6. Funaro, D. (1992). Polynomial Approximation of Differential Equations, Springer-Verlag.
7. Gottlieb, D. and Orszag, S. A. (1977). Numerical Analysis of Spectral Methods: Theory and Applications, SIAM-CBMS.
8. Greengard, L. (1991). Spectral integration and two-point boundary value problem. SIAM J. Numer. Anal. 28, 1071-1080.
9. Hughes, T. J. R. (ed.) (1979). Finite Element Method for Convection Dominated Flows, AMD Vol. 34, Am. Soc. Mech. Eng.
10. Kalinay De Rivas, E. (1972). On the use of nonlinear grids in finite-difference equations. J. Comput. Phys. 10, 202-210.
11. Liu, W. B., and Tang, T. (1994a). A new boundary layer resolving spectral method. AMS Proc. Symp. in Applied Math. 48 (Gautschi, W. (ed.)), 323-326.
12. Liu, W. B., and Tang, T. (1994b). Error analysis for boundary resolving spectral methods. Research Report 94-04, Dept. of Math. and Stats, Simon Fraser University B.C., Canada.
13. Mackenzie, J. A. and Morton, K. W. (1990). Finite volume solution of convection-diffusion test problems. Math. Comp. 60, 189-220.
14. Oriordan, E., and Stynes, M. (1991). A Globally uniformly convergent finite element method for a singularly perturbed elliptic problem in two dimensions. Math. Comp. 57, 47-62.
15. Orszag, S. A., and Israeli, M. (1974). Numerical simulation of viscous incompressible flows. Ann. Rev. Fluid Mech. 6, 281-318.
16. Schwab, C., and Suri, M. (1996). The p and hp versions of the finite element method for problems with boundary layers. Math. Comp. 65, 1403-1429.
17. Shen, J. (1994). Efficient spectral-Galerkin method I. Direct solvers for the second and fourth order equations using Legendre polynomials. SIAM J. Sci. Comput. 15, 1489-1505.
18. Shen, J. (1996). Efficient Chebychev-Legendre-Galerkin methods for elliptic problems. Proceedings of ICOSAHOM'95, 233-239, Houston J. Math.
19. Szegö, G. (1975). Orthogonal Polynomials, AMS Coll. Publ. Vol. 23, Providence.
20. Tang, T., and Trummer, M. R. (1996). Boundary layer resolving pseudospectral method for singular perturbation problems. SIAM J. Sci. Comput. 17, 430-438.