Parameter-uniform approximations for a singularly perturbed convection-diffusion problem with a discontinuous initial condition
Abstract
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. A particular complimentary error function is identified which matches the discontinuity in the initial condition. The difference between this analytical function and the solution of the parabolic problem is approximated numerically. A co-ordinate transformation is used so that a layer-adapted mesh can be aligned to the interior layer present in the solution. Numerical analysis is presented for the associated numerical method, which establishes that the numerical method is a parameter-uniform numerical method. Numerical results are presented to illustrate the pointwise error bounds established in the paper.
Cite
@article{arxiv.2010.09307,
title = {Parameter-uniform approximations for a singularly perturbed convection-diffusion problem with a discontinuous initial condition},
author = {Jose Luis Gracia and Eugene O'Riordan},
journal= {arXiv preprint arXiv:2010.09307},
year = {2022}
}
Comments
28 pages; 2 figures