(untitled) (Communications in Computational Physics, 2024)
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.