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An Adaptive Grid Method for Singularly Perturbed Time-Dependent Convection-Diffusion Problems

Part of: Numerical analysis: Ordinary differential equations

Published online by Cambridge University Press:  02 November 2016

Yanping Chen  and
Li-Bin Liu
Yanping Chen*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
Li-Bin Liu
Affiliation:
School of Mathematics and Computer, Chizhou University, Chizhou, Anhui 247000, China
*
*Corresponding author. Email address:yanpingchen@scnu.edu.cn (Y. Chen)
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Abstract

In this paper, we study the numerical solution of singularly perturbed time-dependent convection-diffusion problems. To solve these problems, the backward Euler method is first applied to discretize the time derivative on a uniform mesh, and the classical upwind finite difference scheme is used to approximate the spatial derivative on an arbitrary nonuniform grid. Then, in order to obtain an adaptive grid for all temporal levels, we construct a positive monitor function, which is similar to the arc-length monitor function. Furthermore, the ε-uniform convergence of the fully discrete scheme is derived for the numerical solution. Finally, some numerical results are given to support our theoretical results.

Keywords

Uniform convergencesingularly perturbedconvection-diffusion problemsadaptive gridan upwind finite difference scheme

MSC classification

Secondary: 65L10: Boundary value problems 65L12: Finite difference methods 65L50: Mesh generation and refinement
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 5 , November 2016 , pp. 1340 - 1358
Copyright
Copyright © Global-Science Press 2016 

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