On the monotonicity of $Q^2$ spectral element method for Laplacian on quasi-uniform rectangular meshes
Numerical Analysis
2023-10-25 v1 Numerical Analysis
Abstract
The monotonicity of discrete Laplacian implies discrete maximum principle, which in general does not hold for high order schemes. The spectral element method has been proven monotone on a uniform rectangular mesh. In this paper we prove the monotonicity of the spectral element method on quasi-uniform rectangular meshes under certain mesh constraints. In particular, we propose a relaxed Lorenz's condition for proving monotonicity.
Keywords
Cite
@article{arxiv.2310.15341,
title = {On the monotonicity of $Q^2$ spectral element method for Laplacian on quasi-uniform rectangular meshes},
author = {Logan J. Cross and Xiangxiong Zhang},
journal= {arXiv preprint arXiv:2310.15341},
year = {2023}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2010.07282