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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
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
publisher
World Scientific
external identifiers
  • wos:000313428600004
  • scopus:84872314328
ISSN
1793-6969
DOI
10.1142/S0219876212500478
language
English
LU publication?
yes
id
fb3e2099-fe6b-499f-9bbd-060873be48f5 (old id 3492277)
date added to LUP
2013-02-26 13:55:59
date last changed
2017-01-01 03:39:59
@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.},
  articleno    = {1250047},
  author       = {Kadalbajoo, M. K. and Singh Yadaw, Arjun},
  issn         = {1793-6969},
  keyword      = {Singular perturbation,boundary layer,Shishkin mesh,finite element,method,reaction-diffusion},
  language     = {eng},
  number       = {4},
  publisher    = {World Scientific},
  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},
  volume       = {9},
  year         = {2012},
}