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arXiv · 2310.15341

On the monotonicity of $Q^2$ spectral element method for Laplacian on quasi-uniform rectangular meshes

Logan J. Cross·Xiangxiong Zhang
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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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Logan J. Cross, Xiangxiong Zhang. 2023-10-23. On the monotonicity of $Q^2$ spectral element method for Laplacian on quasi-uniform rectangular meshes. https://arxiv.org/abs/2310.15341

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