  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.
