Uniformly convergent finite volume difference scheme for 2D convection-dominated problem with discontinuous coefficients

Applied Mathematics and Computation

Volumn 163, Issue 2, 2005, Pages 645-665

  Brayanov, Iliya A ^a  

^a UNIVERSITY OF RUSE   (Bulgaria)

Author keywords

Asymptotic analysis; Convection diffusion problems; Finite volume methods; Modified upwind approximations; Shishkin mesh; Singular perturbation; Uniform convergence

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; DIFFUSION; FINITE VOLUME METHOD; HEAT CONVECTION; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES;

ASYMPTOTIC ANALYSIS; CONVECTION-DIFFUSION PROBLEMS; MODIFIED UPWIND APPROXIMATIONS; SHISHKIN MESHES; SINGULAR PERTURBATION; UNIFORM CONVERGENCE;

PROBLEM SOLVING;

EID: 13544258647     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.04.007     Document Type: Article

References (17)

1. V.B. Andreev, Anisotropic estimates for the discrete Green's function of a monotone difference operator in the singularly perturbed case and its application, Preprint TU Dresden, Math-NM-06-2000, 2000
2. V.B. Andreev, Green's function and uniform convergence of monotone difference schemes for a singularly perturbed convection-diffusion equation on Shishkin's mesh in one and two dimensions, DCU Maths. Dept. Preprint Series, MS-01-15, 2001
3. Andreev V.B., Savin I.A. On the uniform convergence of the monotone Samarski's scheme and its modification. Comput. Math. Math. Phys. 35(5):1995;739-752
4. Braianov I.A., Vulkov L.G. Uniform in a small parameter convergence of Samarskii's monotone scheme and its modification for the convection-diffusion equation with a concentrated source. Comput. Math. Math. Phys. 40(4):2000;534-550
5. Braianov I.A., Vulkov L.G. Numerical solution of a reaction-diffusion elliptic interface problem with strong anisotropy. Computing. 71(2):2003;153-173
6. I.A. Brayanov, L.G. Vulkov, Finite volume difference methods for convection-dominated problems with interface. Springer-Verlag, Lecture Notes in Comp. Sci. 2907 (2004) 429-437
7. P.A. Farrel, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin, Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient, Preprint MS-01-06, School of Mathematical Sciences, Dublin City University, 2001
8. Lazarov R.D., Michev I.D., Vassilevski P.S. Finite volume methods for convection-diffusion problems. SIAM J. Numer. Anal. 33(1):1996;31-55
9. Linss T. Finite difference schemes for convection-diffusion problems with a concentrated source and discontinuous convection field. Comput. Methods Appl. Math. 2(1):2002;41-49
10. Linss T. Uniform pointwise convergence of an upwind finite volume method on layer-adapted meshes. ZAMM. 82(4):2002;247-254
11. Linss T., Stynes M. Asymptotic analysis and Shishkin-type decomposition for an elliptic convection-diffusion problem. J. Math. Anal. Appl. 261:2001;604-632
12. Miller J.J.H., O'Riordan E., Shishkin G.I. Fitted Numerical Methods for Singular Perturbation Problems. 1996;World Scientific, Singapore
13. Roos H.-G., Stynes M., Tobiska L. Numerical Methods for Singularly Perturbed Differential Equations. 1996;Springer-Verlag, Berlin
14. Roos H.-G., Zarin H. The streamline-diffusion method for a convection-diffusion problem with a point source. J. Comput. Appl. Math. 150:2003;109-128
15. Samarskii A.A. Theory of Difference Schemes. 1983;Nauka, Moscow. (in Russian)
16. G.I. Shishkin, Grid approximations of singularly perturbed elliptic and parabolic equations, Ural Branch, Russian Academy of Sciences, Ekaterinburg, 1992 (in Russian)
17. Vasil'eva A.B., Butuzov V.F. Asymptotic Methods in Singular Perturbation Theory. 1996;Vysshaya Shkola, Moscow. (in Russian)