192
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Numerical methods for singularly perturbed elliptic problems containing two perturbation parametersFootnote1

, &
Pages 199-212 | Received 15 Oct 2005, Published online: 14 Oct 2010

References

  • Clavero , C. , Gracia , J.L. and E&O;apos , E. 2005 . A parameter robust numerical method for a two dimensional reaction‐diffusion problem . Mathematics of Computation , 74 : 1743 – 1758 .
  • Farrell , P.A. , Hegarty , A.F. , Miller , J.J.H. , O'Riordan , E. and Shishkin , G.I. 2000 . Robust computational techniques for boundary layers , Boca Raton : Chapman and Hall/CRC Press .
  • Han , H. and Kellogg , R.B. 1990 . Differentiability properties of solutions of the equation ‐#ANA2#AUAu + ru = f(x,y) in a square . SIAM J. Math Anal. , 21 : 394 – 408 .
  • Ladyzhenskaya , O.A. and Ural'tseva , N.N. 1968 . Linear and Quasilinear Elliptic Equations , New York and London : Academic Press .
  • Linß , T. and Stynes , M. 2001 . Asymptotic analysis and Shishkin‐type decomposition for an elliptic convection‐diffusion problem . J. Math. Anal, and Applications , 261 : 604 – 632 .
  • O'Riordan , E. , Pickett , M.L. and Shishkin , G.I. Parameter‐uniform finite difference schemes for singularly perturbed parabolic diffusion‐convection‐reaction problems . Mathematics of Computation , (to appear)
  • O'Riordan , E. , Pickett , M.L. and Shishkin , G.I. 2003 . Singularly perturbed problems modeling reaction‐convection‐diffusion processes . Computational Methods in Applied Mathematics , 3 (3) : 424 – 442 .
  • Roos , H.‐G. and Uzelac , Z. 2003 . The SDFEM for a convection diffusion problem with two small parameters . Computational Methods in Applied Mathematics , 3 (3) : 1 – 16 .
  • Shishkin , G.I. 1992 . Discrete approximation of singularly perturbed elliptic and parabolic equations , Ural Section, Ekaterinburg : Russian Academy of Sciences . (in Russian)
  • Shishkin , G.I. and Titov , V.A. 1976 . A difference scheme for a differential equation with two small parameters at the derivatives . Chisl. Metody Meh. Sploshn. Sredy , 7 (2) : 145 – 155 . (in Russian)
  • Titov , V.A. and Shishkin , G.I. 1976 . A numerical solution of a parabolic equation with small parameters multiplying the derivatives with respect to the space variables . Trudy Inst. Mat. i Meh. Ural Nauchn. Centr Akad. Nauk SSSR , 21 : 38 – 43 . (in Russian)
  • This research was supported in part by the National Center for Plasma Science and Technology Ireland and by the Russian Foundation for Basic Research grant No. 04–01–00578.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.