TY - JOUR
T1 - On the Monotonicity of $Q^2$ Spectral Element Method for Laplacian on Quasi-Uniform Rectangular Meshes
AU - Cross , Logan J.
AU - Zhang , Xiangxiong
JO - Communications in Computational Physics
VL - 1
SP - 160
EP - 180
PY - 2024
DA - 2024/01
SN - 35
DO - http://doi.org/10.4208/cicp.OA-2023-0206
UR - https://global-sci.org/intro/article_detail/cicp/22899.html
KW - Inverse positivity, discrete maximum principle, high order accuracy, monotonicity, discrete Laplacian, quasi uniform meshes, spectral element method.
AB - <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>