IJPAM: Volume 55, No. 2 (2009)

PARAMETER-UNIFORM RITZ-GALERKIN FINITE ELEMENT
METHOD FOR TWO PARAMETER SINGULARLY
PERTURBED BOUNDARY VALUE PROBLEMS

Mohan K. Kadalbajoo$^1$, Arjun Singh Yadaw$^2$
$^{1,2}$Department of Mathematics and Statistics
Indian Institute of Technology
Kanpur, Kanpur, 208016, INDIA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.A singularly perturbed reaction-diffusion problem with two small parameters is considered. Due to these two small parameters boundary layers exist. To resolve the boundary layers a piecewise-uniform Shishkin mesh has been taken and we have shown that the Ritz-Galerkin method has almost second order parameters-uniform convergence. Numerical experiments support these theoretical results.

Received: August 14, 2009

AMS Subject Classification: 34K26, 65L60, 30E25, 65L50

Key Words and Phrases: singular perturbation, reaction-diffusion, boundary value problems, Ritz-Galerkin method, Shishkin mesh

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 2