On the Monotonicity of $Q^2$ Spectral Element Method for Laplacian on Quasi-Uniform Rectangular Meshes
DOI:
https://doi.org/10.4208/cicp.OA-2023-0206Keywords:
Inverse positivity, discrete maximum principle, high order accuracy, monotonicity, discrete Laplacian, quasi uniform meshes, spectral element method.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.