| 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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