@Article{IJNAM-4-1,
author = {},
title = {An $\varepsilon$-Uniform Finite Element Method for Singularly Perturbed Two-Point Boundary Value Problems},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2007},
volume = {4},
number = {1},
pages = {127--140},
abstract = {<p style="text-align: justify;">This work develops an $\varepsilon$-uniform finite element method
for singularly perturbed two-point boundary value problems. A surprising
and remarkable observation is illustrated: By inserting one node
arbitrarily in any element, the new finite element solution always
intersects with the original one at fixed points, and the errors at
those points converge at the same rate as regular boundary value
problems (without boundary layers). Using this fact, an effective $\varepsilon$-uniform approximation out of boundary layer is proposed by
adding one point only in the element that contains the boundary layer.
The thickness of the boundary layer need not be known a priori.
Numerical results are carried out and compared to the Shishkin mesh for
demonstration purpose.</p>},
issn = {2617-8710},
doi = {https://doi.org/2007-IJNAM-855},
url = {https://global-sci.com/article/83762/an-varepsilon-uniform-finite-element-method-for-singularly-perturbed-two-point-boundary-value-problems}
}