@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 = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.240315.301215a},
url = {http://global-sci.org/intro/article_detail/cicp/11192.html}
}