On the Monotonicity of $Q^2$ Spectral Element Method for Laplacian on Quasi-Uniform Rectangular Meshes

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.

Author Details

Logan J. Cross

Xiangxiong Zhang