Year: 2016
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 3 : pp. 319–343
Abstract
We develop high-order Galerkin methods with graded meshes for solving the two-dimensional reaction-diffusion problem on a rectangle. With the help of the comparison principle, we establish upper bounds for high order partial derivatives of an arbitrary order of its exact solution. According to prior information of the high order partial derivatives of the solution, we design both implicit and explicit graded meshes which lead to numerical solutions of the problem having an optimal convergence order. Numerical experiments are presented to confirm the theoretical estimate and to demonstrate the outperformance of the proposed meshes over the Shishkin mesh.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-IJNAM-442
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 3 : pp. 319–343
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Singularly perturbation reaction-diffusion problem priori estimates graded meshes Galerkin method.