The use of defect correction for the solution of parabolic singular perturbation problems

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 77, Issue 1, 1997, Pages 59-74

  Hemker, P W ^a   Shishkin, G I ^b   Shishkina, L P ^c  

^a CWI   (Netherlands)

^b INSTITUTE OF MATHEMATICS AND MECHANICS   (Russian Federation)

^c Scientific Research Institute of Heavy Machine Building   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002240887     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.19970770111     Document Type: Article

References (14)

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2. BÖHMER, K.; HEMKER, P. W.; STETTER, H. J.: The defect correction approach. In BÖHMER, K.; STETTER, H. J. (eds.): Defect correction methods: Theory and applications. Computing Suppl. 5 (1984), 1-32.
3. CLARLET, P.: The finite element method for elliptic problems. North-Holland Publishing Company 1978.
4. DOOLAN, E. P.; MILLER, J. J. H.; SCHILDERS, W. H. A.: Uniform numerical methods for problems with initial and boundary layers. Dublin 1980.
5. HEMKER, P. W.: Numerical aspects of singular perturbation problems. In VERHULST, F. (ed.): Asymptotic analysis. II. Lecture Notes in Mathematics Nr. 985, Springer Verlag, Berlin etc. 1983, pp. 267-287.
6. HEMKER, P. W.; SHISHKIN, G. I.: On a class of singularly perturbed boundary value problems for which an adaptive mesh technique is necessary. In BAINOV, D.; KOVACHEV, V. (eds.): Proc. Second Internat. Colloq. on Numerical Analysis. VSP, International Science Publishers, Utrecht, The Netherlands 1994, pp. 83-92.
7. LADYZHENSKAYA, O. A.; SOLONNIKOV, V. A.; URAL'TSEVA, N. N.: Linear and quasi-linear equations of parabolic type. AMS 1968.
8. MARCHUK, G. I.: Methods of numerical mathematics. Springer, New York 1982.
9. SAMARSKY, A. A.: Theory of difference schemes. Nauka, Moscow 1989 (in Russian).
10. SHISHKIN, G. I: Difference scheme on a non-uniform grid for the differential equation with a small parameter at the highest derivative. Zhurn. Vychisl. Mat. Mat. Fiz. 23 (1983), 609-619 (in Russian).
11. SHISHKIN, G. I.: Approximation of solutions to singularly perturbed boundary value problems with corner boundary layers. Zhurn. Vychisl. Mat. Mat. Fiz. 27 (1987), 1360-1374 (in Russian).
12. SHISHKIN, G. I.: Approximation of solutions to singularly perturbed boundary value problems with parabolic boundary layers. Zhurn. Vychisl. Mat. Mat. Fiz. 29 (1989), 963-977 (in Russian).
13. SHISHKIN, G. I.: Grid approximation of singularly perturbed elliptic equation in domain with characteristic bounds. Soviet J. Numer. Anal. Math. Modelling 5 (1990), 327-343.
14. SHISHKIN, G. I.: Grid approximation of singularly perturbed elliptic and parabolic equations. Ur. O. RAN, Ekaterinburg 1992 (in Russian).