Title Parameter-Uniform finite element method for two-parameter singularly perturbed parabolic reaction-diffusion problems
Authors M. K. Kadalbajoo, Arjun Singh Yadaw
Alternative Location http://dx.doi.org/10.1142/S..., Restricted Access
Publication International Journal of Computational Methods
Year 2012
Volume 9
Issue 4
Pages
Document type Article
Status Published
Quality controlled Yes
Language eng
Publisher World Scientific Publishing
Abstract English 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.
Keywords Singular perturbation, boundary layer, Shishkin mesh, finite element, method, reaction-diffusion,
ISBN/ISSN/Other ISSN: 0219-8762

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