Numerical Solution of a Reaction-Diffusion Elliptic Interface Problem with Strong Anisotropy

Computing (Vienna/New York)

Volumn 71, Issue 2, 2003, Pages 153-173

  Braianov, I ^a   Vulkov, L ^a  

^a UNIVERSITY OF RUSE   (Bulgaria)

Author keywords

Elliptic interface problems; Finite volume method; Reaction diffusion; Shishkin mesh; Singular perturbation

Indexed keywords

ANISOTROPY; DIFFUSION; FINITE ELEMENT METHOD; FINITE VOLUME METHOD; PERTURBATION TECHNIQUES;

SINGULAR PERTURBATION;

PROBLEM SOLVING;

EID: 0242498730     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00607-003-0009-3     Document Type: Article

References (17)

1. Bastian, P., Wittum, G.: On robust and adaptive multigrid methods. In: Hemker, P.W. et al. (eds) "Multigrid Methods": Proceed. of the 4-th European Multigrid Conference, p 1-19, Basel 1994.
2. Braianov, I., Vulkov, L.: Asymptotic analysis and shishkin decomposition for an anisotropic reaction-diffusion elliptic interface problem. (submitted).
3. Chavent, G., Jaffre, J.: Mathematical models and finite elements for reservoir simulation: single phase, multiphase and multi component flows through porous media. Amsterdam: North-Holland 1986.
4. Finite volumes for complex applications II. Problems and Perspectives. Vilsmeier, R. Benkhaldoun, F. Hänel, D. (eds.): Hermes Science Publications, Paris 1999.
5. Han, H., Kellogg, R. B.: Differentiability properties of solutions of the equations -εu + ru = f(x, y) in a square. SIAM J. Math. Anal. 21, 394-408 (1990).
6. Kopteva, N. V.: The two dimensional Sobolev inequality in the case of an arbitrary grid. Comp. Math. Math. Phys. 38(4), 574-577 (1998).
7. Ladyzhenskaya, O. A., Rivkind, V. J., Ural'ceva, N. N.: The classical solvability of diffraction problems. Trudy Mat. Inst. Steklov 92, 116-146 (1966). Translated In: Proceed. of Steklov Inst. of Math. 92, Boundary value problems of mathematical physics IV. Am. Math. Soc. (1966).
8. Ladyzhenskaya, O. A., Rivkind, V. J., Ural'ceva, N. N.: The classical solvability of diffraction problems. Trudy Mat. Inst. Steklov 92, 116-146 (1966). Translated In: Proceed. of Steklov Inst. of Math. 92, Boundary value problems of mathematical physics IV. Am. Math. Soc. (1966).
9. Li, J.: Quasioptimal uniformly convergent finite element methods for the elliptic boundary layer problem. Computers Math. Applic. 33(10), 11-22 (1997).
10. Linß, T., Stynes, M.: Asymptotic analysis and Shishkin-type decomposition for an elliptic convection-diffusion problem. J. of Math. Anal. Appl. 261, 604-632 (2001).
11. Miller, J. J. H., O'Riordan, E., Shishkin, G. I.: Fitted numerical methods for singular perturbation problems. Singapore: World scientific 1996.
12. Oganesyan, L. A., Ruhovetc, L. A.: Variational difference methods for solution of elliptic equations. AN. Arm. SSR, 1979 (in Russian).
13. Roos, H.-G., Stynes, M., Tobiska, L.: Numerical Methods for singularly perturbed differential equations. Berlin: Springer-Verlag 1996.
14. Samarskii, A. A.: Theory of difference schemes. Moscow: Nauka 1977 (in Russian).
15. Shishkin, G. I.: Grid approximations of singularly perturbed elliptic and parabolic equations. Ural Branch, Russian Academy of Sciences, Ekaterinburg, 1992 (in Russian).
16. Stynes, M.: Finite volume method for convection-diffusion problems. J. of Comp. and Appl. Math. 63, 83-90 (1994).
17. Vasil'eva, A. B., Butuzov, V. F.: Asymptotic methods in singular perturbation theory. Moscow: Vysshaya Shkola 1996 (in Russian).