@Article{CiCP-35-160,
author = {Cross , Logan J. and Zhang , Xiangxiong},
title = {On the Monotonicity of $Q^2$ Spectral Element Method for Laplacian on Quasi-Uniform Rectangular Meshes},
journal = {Communications in Computational Physics},
year = {2024},
volume = {35},
number = {1},
pages = {160--180},
abstract = {<p style="text-align: justify;">The monotonicity of discrete Laplacian implies discrete maximum principle, which in general does not hold for high order schemes. The $Q^2$ spectral element
method has been proven monotone on a uniform rectangular mesh. In this paper we
prove the monotonicity of the $Q^2$ spectral element method on quasi-uniform rectangular meshes under certain mesh constraints. In particular, we propose a relaxed Lorenz’s
condition for proving monotonicity.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0206},
url = {http://global-sci.org/intro/article_detail/cicp/22899.html}
}