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

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

Year:    2016

Communications in Computational Physics, Vol. 20 (2016), Iss. 5 : pp. 1340–1358

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.240315.301215a

Communications in Computational Physics, Vol. 20 (2016), Iss. 5 : pp. 1340–1358

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords: