Parameter-Uniform finite element method for two-parameter singularly perturbed parabolic reaction-diffusion problems
(2012) In International Journal of Computational Methods 9(4).- Abstract
- In this paper, parameter-uniform numerical methods for a class of singularly perturbed one-dimensional parabolic reaction-diffusion problems with two small parameters on a rectangular domain are studied. Parameter-explicit theoretical bounds on the derivatives of the solutions are derived. The method comprises a standard implicit finite difference scheme to discretize in temporal direction on a uniform mesh by means of Rothe's method and finite element method in spatial direction on a piecewise uniform mesh of Shishkin type. The method is shown to be unconditionally stable and accurate of order O(N-2(ln N)(2) + Delta t). Numerical results are given to illustrate the parameter-uniform convergence of the numerical approximations.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3492277
- author
- Kadalbajoo, M. K. and Singh Yadaw, Arjun LU
- organization
- publishing date
- 2012
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Singular perturbation, boundary layer, Shishkin mesh, finite element, method, reaction-diffusion
- in
- International Journal of Computational Methods
- volume
- 9
- issue
- 4
- article number
- 1250047
- publisher
- World Scientific Publishing
- external identifiers
-
- wos:000313428600004
- scopus:84872314328
- ISSN
- 1793-6969
- DOI
- 10.1142/S0219876212500478
- language
- English
- LU publication?
- yes
- additional info
- The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
- id
- fb3e2099-fe6b-499f-9bbd-060873be48f5 (old id 3492277)
- date added to LUP
- 2016-04-01 10:31:23
- date last changed
- 2022-04-20 03:02:00
@article{fb3e2099-fe6b-499f-9bbd-060873be48f5, abstract = {{In this paper, parameter-uniform numerical methods for a class of singularly perturbed one-dimensional parabolic reaction-diffusion problems with two small parameters on a rectangular domain are studied. Parameter-explicit theoretical bounds on the derivatives of the solutions are derived. The method comprises a standard implicit finite difference scheme to discretize in temporal direction on a uniform mesh by means of Rothe's method and finite element method in spatial direction on a piecewise uniform mesh of Shishkin type. The method is shown to be unconditionally stable and accurate of order O(N-2(ln N)(2) + Delta t). Numerical results are given to illustrate the parameter-uniform convergence of the numerical approximations.}}, author = {{Kadalbajoo, M. K. and Singh Yadaw, Arjun}}, issn = {{1793-6969}}, keywords = {{Singular perturbation; boundary layer; Shishkin mesh; finite element; method; reaction-diffusion}}, language = {{eng}}, number = {{4}}, publisher = {{World Scientific Publishing}}, series = {{International Journal of Computational Methods}}, title = {{Parameter-Uniform finite element method for two-parameter singularly perturbed parabolic reaction-diffusion problems}}, url = {{http://dx.doi.org/10.1142/S0219876212500478}}, doi = {{10.1142/S0219876212500478}}, volume = {{9}}, year = {{2012}}, }