TY - JOUR
T1 - Uniform Convergence Analysis for Singularly Perturbed Elliptic Problems with Parabolic Layers
AU - Jichun Li & Yitung Chen
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 138
EP - 149
PY - 2008
DA - 2008/01
SN - 1
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/nmtma/6045.html
KW - Finite element methods, singularly perturbed problems, uniformly convergent.
AB - <p style="text-align: justify;">In this paper, using Lin&#39;s integral identity technique, we
prove the optimal uniform convergence
 $O(N_x^{-2}\ln^2N_x+N_y^{-2}\ln^2N_y)$ in the $L^2$-norm
 for singularly perturbed problems with parabolic layers.
The error estimate is achieved by bilinear finite elements on a
Shishkin type mesh. Here $N_x$ and $N_y$ are the number of elements
in the $x$- and $y$-directions, respectively. Numerical results are
provided supporting our theoretical analysis.</p>