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Parameter-Uniform finite element method for two-parameter singularly perturbed parabolic reaction-diffusion problems

Kadalbajoo, M. K. and Singh Yadaw, Arjun LU (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.
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author
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organization
publishing date
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}},
}