A uniformly accurate finite-element method for a singularly perturbed one-dimensional reaction-diffusion problem

Mathematics of Computation

Volumn 47, Issue 176, 1986, Pages 555-570

  Stynes, Martin ^b  

^a Regional Technical College   (Ireland)

^b UNIVERSITY COLLEGE CORK   (Ireland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84966211358     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1986-0856702-7     Document Type: Article

References (13)

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2. E. P. DOOLAN, J. J. H. MILLER & W. H. A. SCHILDERS, Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole Press, Dublin, 1980.
3. P. P. N. DE GROEN, "A finite element method with a large mesh width for a stiff two-point boundary value problem, " J. Comput. Appl. Math., v. 7, 1981, pp. 3-15.
4. A. F. HEGARTY, J. J. H. MILLER & E. ORIORDAN, "Uniform second order différence schemes for singular perturbation problems, " Boundary and Interior Loyers-Computational and Asymptotic Methods(J. J. H. Miller, ed.), Boole Press, Dublin, 1980, pp. 301-305.
5. P. W. Hemker, A Numerical Study of Stiff Two-point Boundary Value Problems, Mathematical Centre Tracts, No. 80, Amsterdam, 1977.
6. J. J. H. Miller, "On the convergence, uniformly in e, of différence schemes for a two-point boundary value singular perturbation problem, " Numerical Analysis of Singular Perturbation Problems (P. W. Hemker & J. J. H. Miller, eds.), Academic Press, New York, 1979, pp. 467-474.
7. K. Niijima, "On a three-point différence scheme for a singular perturbation problem without a first derivative term I, " Mem. Numer. Math., v. 7, 1980, pp. 1-10.
8. M. A. PROTTER & H. F. WEINBERGER, Maximum Principies in Differential Equations, Prentice-Hall, Englewood Cliffs, N. J., 1967.
9. E. O'Riordan, Finite Element Methods for Singularly Perturbed Problems, Ph.D. thesis, School of Mathematics, Trinity College, Dublin, 1982.
10. A. H. SCHATZ & L. B. WAHLBIN, "On the finite element method for singularly perturbed reaction-diffusion problems in two and one dimensions, " Math. Comp., v. 40, 1983, pp. 47-89.
11. G. I. Shishkin, "A différence scheme on a non-uniform mesh for a differential équation with a small parameter in the highest derivative, " U.S.S.R. Comput. Math, and Math. Phys., v. 23, no. 3, 1983, pp. 59-66.
12. M. STYNES & E. O‘RIORDAN, "A superconvergence resuit for a singularly perturbed boundary value problem, " BAIL III-Proc. Third International Conference on Boundary and Interior Layers (J. J. H. Miller, ed.), Boole Press, Dublin, 1984, pp. 309-313.
13. R. S. VARGA, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, N. J., 1962.