## A parameter robust numerical method for a two dimensional reaction-diffusion problem

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- by C. Clavero, J. L. Gracia and E. O’Riordan PDF
- Math. Comp.
**74**(2005), 1743-1758 Request permission

## Abstract:

In this paper a singularly perturbed reaction-diffusion partial differential equation in two space dimensions is examined. By means of an appropriate decomposition, we describe the asymptotic behaviour of the solution of problems of this kind. A central finite difference scheme is constructed for this problem which involves an appropriate Shishkin mesh. We prove that the numerical approximations are almost second order uniformly convergent (in the maximum norm) with respect to the singular perturbation parameter. Some numerical experiments are given that illustrate in practice the theoretical order of convergence established for the numerical method.## References

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## Additional Information

**C. Clavero**- Affiliation: Departamento de Matemática Aplicada, Universidad de Zaragoza, Zaragoza, Spain
- Email: clavero@unizar.es
**J. L. Gracia**- Affiliation: Departamento de Matemática Aplicada, Universidad de Zaragoza, Teruel, Spain
- Email: jlgracia@unizar.es
**E. O’Riordan**- Affiliation: School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland
- Email: eugene.oriordan@dcu.ie
- Received by editor(s): May 19, 2004
- Published electronically: June 7, 2005
- Additional Notes: This research was partially supported by the Diputación General de Aragón and the project MCYT/FEDER BFM2001–2521
- © Copyright 2005 American Mathematical Society
- Journal: Math. Comp.
**74**(2005), 1743-1758 - MSC (2000): Primary 65N06, 65N12, 65N15; Secondary 35J25
- DOI: https://doi.org/10.1090/S0025-5718-05-01762-X
- MathSciNet review: 2164094