Optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction-diffusion boundary-value problems

Das, Pratibhamoy and Natesan, Srinivasan (2014) Optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction-diffusion boundary-value problems. In: APPLIED MATHEMATICS AND COMPUTATION, 249 . pp. 265-277.

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Abstract

In this article, we study the problem of determining an appropriate grading of meshes for a system of coupled singularly perturbed reaction-diffusion problems having diffusion parameters with different magnitudes. The central difference scheme is used to discretize the problem on adaptively generated mesh where the mesh equation is derived using an equidistribution principle. An a priori monitor function is obtained from the error estimate. A suitable a posteriori analogue of this monitor function is also derived for the mesh construction which will lead to an optimal second-order parameter uniform convergence. We present the results of numerical experiments for linear and semilinear reaction-diffusion systems to support the effectiveness of our preferred monitor function obtained from theoretical analysis. (C) 2014 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Publication:	APPLIED MATHEMATICS AND COMPUTATION
Additional Information:	Copyright for this article belongs to the ELSEVIER SCIENCE INC, 360 PARK AVE SOUTH, NEW YORK, NY 10010-1710 USA
Department/Centre:	Division of Interdisciplinary Sciences > Supercomputer Education & Research Centre
Date Deposited:	12 Jan 2015 10:31
Last Modified:	12 Jan 2015 10:31
URI:	http://eprints.iisc.ac.in/id/eprint/50626

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