@Article{IJNAM-17-297,
author = {Russell , Stephen and Madden , Niall},
title = {Analysis of a Galerkin Finite Element Method Applied to a Singularly Perturbed Reaction-Diffusion Problem in Three Dimensions},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2020},
volume = {17},
number = {3},
pages = {297--315},
abstract = {<p style="text-align: justify;">We consider a linear singularly perturbed reaction-diffusion problem in three dimensions and its numerical solution by a Galerkin finite element method with trilinear elements. The problem is discretised on a Shishkin mesh with $N$ intervals in each coordinate direction. Derivation of an error estimate for such a method is usually based on the (Shishkin) decomposition of the solution into distinct layer components. Our contribution is to provide a careful and detailed analysis of the trilinear interpolants of these components. From this analysis it is shown that, in the usual energy norm the errors converge at a rate of $\mathcal{O}$($N$<sup>−2</sup>+$ε$<sup>1/2</sup>$N$<sup>−1</sup>ln$N$). This is validated by numerical results.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/16860.html}
}