A note on the energy norm for a singularly perturbed model problem

Computing (Vienna/New York)

Volumn 69, Issue 3, 2002, Pages 265-272

  Kunert, Gerd ^a  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Adaptive algorithm; Error estimator; Reaction diffusion equation; Singularly perturbed problem

Indexed keywords

ADAPTIVE ALGORITHMS; COMPUTER SIMULATION; MATHEMATICAL OPERATORS; PERTURBATION TECHNIQUES;

REACTION DIFFUSION EQUATIONS;

PROBLEM SOLVING;

EID: 0036955382     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00607-002-1457-x     Document Type: Article

References (14)

1. Ainsworth M., Babuška, I.: Reliable and robust a posteriori error estimation for singularly perturbed reaction-diffusion problems. SIAM J. Num. Anal. 36(2), 331-353 (1999).
2. Angermann, L.: Balanced a posteriori error estimates for finite volume type discretizations of convection-dominated elliptic problems. Computing 55(4), 305-323 (1995).
3. John, V.: A numerical study of a posteriori error estimators for convection-diffusion equations. Comput. Methods Appl. Mech. Engrg. 190, 757-781 (2000).
4. Kay, D., Silvester, D.: The reliability of local error estimators for convection-diffusion equations. IMA J. Numer. Anal. 21(1), 107-122 (2001).
5. Kunert, G.: A note on the energy norm for a singularly perturbed model problem. Preprint SFB393/01-02, TU Chemnitz, January 2001. (http://archiv.tu-chemnitz.de/pub/2001/0006/index.html.)
6. Kunert, G.: Robust a posteriori error estimation for a singularly perturbed reaction-diffusion equation on anisotropic tetrahedral meshes. Adv. Comp. Math. 15(1-4), 237-259 (2001).
7. Kunert, G.: Robust local problem error estimation for a singularly perturbed problem on anisotropic finite element meshes. Math. Model. Numer. Anal. 35(6), 1079-1109 (2001).
8. Maz'ya, V., Nazarov, S., Plamenevskij, B.: Asymptotic theory of elliptic boundary value problems in singularly perturbed domains vol. I and II. Operator Theory: Advances and applications, 111/112. Basel: Birkhäuser 2001. (Translation from German.)
9. Miller, J. J. H., O'Riordan, E., Shishkin, G.: Fitted numerical methods for singularly perturbed problems. Error estimates in the maximum norm for linear problems in one and two dimensions. Singapore: World Scientific Publications 1996.
10. Morton, K. W.: Numerical solution of convection-diffusion problems. London: Chapman & Hall 1996.
11. Papastavrou, A.: Adaptive Finite Element Methoden für Konvektions-Diffusionsprobleme. PhD thesis, Ruhr-Universität Bochum 1998.
12. Papastavrou, A., Verfürth, R.: A posteriori error estimators for stationary convection-diffusion problems: A computational comparison. Comput. Methods Appl. Mech. Eng. 189(2), 449-462 (2000).
13. Roos, H.-G., Stynes, M., Tobiska, L.: Numerical methods for singularly perturbed differential equations. Convection-diffusion and flow problems. Berlin: Springer 1996.
14. Verfürth, R.: Robust a posteriori error estimators for singularly perturbed reaction-diffusion equations. Numer. Math. 78(3), 479-493 (1998).