A note on the conditioning of upwind schemes on Shishkin meshes

IMA Journal of Numerical Analysis

Volumn 16, Issue 4, 1996, Pages 529-538

  Roos, Hans Görg ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

CONVECTION DIFFUSION; DISCRETIZATIONS; NUMERICAL EXPERIMENTS; SHISHKIN MESHES; SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS; UP-WIND SCHEME;

BOUNDARY VALUE PROBLEMS;

EID: 0030490165     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/16.4.529     Document Type: Article

References (13)

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3. BOHL, E. 1981 Finite Modelle gewöhnlicher Randwertaufgaben. Stuttgart: Teubner.
4. GUO, W., & STYNES, M. 1993 Pointwise error estimates for a streamline diffusion scheme on a Shishkin mesh for a convection-diffusion problem. Preprint 93-2, Department of Mathematics, University College Cork, Ireland.
5. MILLER, J. J. H., O'RIORDAN, E. O., & SHISHKIN, G. I. 1995 Solution of singular perturbation problems with ε-uniform numerical methods - introduction to the theory for linear problems in one and two dimensions. Singapore: World Scientific. To appear.
6. SCHABACK, R., & WERNER, H. 1992 Numerische Mathematik. Berlin: Springer.
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8. SHISHKIN, G. I. 1990 Grid approximation of singularly perturbed elliptic and parabolic equations. Second Doctoral Thesis, Keldysh Institute, Moscow. (In Russian).
9. SHISHKIN, G. I. 1992 Discrete Approximation of Singularly Perturbed Elliptic and Parabolic Equations. Ekatarinenburg: Russian Academy of Science, Ural Section. (In Russian).
10. SUN, G., & STYNES, M. 1995 Finite element methods for singularly perturbed high-order elliptic two-point boundary value problems. I: reaction-diffusion-type problems. IMA J. Numer. Anal. 15, 117-139.
11. ROOS, H. G., STYNES, M., & TOBISKA, L. 1995 Numerical Methods for Singularly Perturbed Differential Equations (Springer Series in computational Mathematics). Berlin: Springer.
12. TOBISKA, L. 1983 Diskretisierungsverfahren zur Lösung singulär gestörter Randwert-probleme. ZAMM 63, 115-123.
13. VULANOVIČ, R. 1986 Mesh construction for discretization of singularly perturbed boundary value problems. PhD Thesis, University Novy Sad.