@Article{IJNAM-13-319,
author = {Z.-W. Li, B. Wu and Y.-S. Xu},
title = {High Order Galerkin Methods with Graded Meshes for Two-Dimensional Reaction-Diffusion Problems},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2016},
volume = {13},
number = {3},
pages = {319--343},
abstract = {<p style="text-align: justify;">We develop high-order Galerkin methods with graded meshes for solving the two-dimensional
reaction-diffusion problem on a rectangle. With the help of the comparison principle,
we establish upper bounds for high order partial derivatives of an arbitrary order of its exact
solution. According to prior information of the high order partial derivatives of the solution,
we design both implicit and explicit graded meshes which lead to numerical solutions of the
problem having an optimal convergence order. Numerical experiments are presented to confirm
the theoretical estimate and to demonstrate the outperformance of the proposed meshes over the
Shishkin mesh.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/442.html}
}