On the Monotonicity of $Q^2$ Spectral Element Method for Laplacian on Quasi-Uniform Rectangular Meshes
Year: 2024
Author: Logan J. Cross, Xiangxiong Zhang
Communications in Computational Physics, Vol. 35 (2024), Iss. 1 : pp. 160–180
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0206
Communications in Computational Physics, Vol. 35 (2024), Iss. 1 : pp. 160–180
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Inverse positivity discrete maximum principle high order accuracy monotonicity discrete Laplacian quasi uniform meshes spectral element method.