Volume 20, Issue 5
An Adaptive Grid Method for Singularly Perturbed Time-Dependent Convection-Diffusion Problems

Yanping Chen & Li-Bin Liu

Commun. Comput. Phys., 20 (2016), pp. 1340-1358.

Published online: 2018-04

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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.

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@Article{CiCP-20-1340, author = {}, title = {An Adaptive Grid Method for Singularly Perturbed Time-Dependent Convection-Diffusion Problems}, journal = {Communications in Computational Physics}, year = {2018}, volume = {20}, number = {5}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.240315.301215a}, url = {http://global-sci.org/intro/article_detail/cicp/11192.html} }
TY - JOUR T1 - An Adaptive Grid Method for Singularly Perturbed Time-Dependent Convection-Diffusion Problems JO - Communications in Computational Physics VL - 5 SP - 1340 EP - 1358 PY - 2018 DA - 2018/04 SN - 20 DO - http://doi.org/10.4208/cicp.240315.301215a UR - https://global-sci.org/intro/article_detail/cicp/11192.html KW - AB -

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.

Yanping Chen & Li-Bin Liu. (2020). An Adaptive Grid Method for Singularly Perturbed Time-Dependent Convection-Diffusion Problems. Communications in Computational Physics. 20 (5). 1340-1358. doi:10.4208/cicp.240315.301215a
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