Time-explicit high order finite element/DG methods for the advection equation tend to have a timestep restriction which looks like$$dt < C h/p^2$$where $h$ is mesh spacing and $p$ is polynomial degree. I'm having trouble finding a similar order-dependent restriction for high order finite difference stencils.  Is there one known, or does it depend more on the specific stencil used instead of the order of the stencil?Edit: Given Kirill's answer, I'll look instead for the growth of $\rho(A)$ as a proxy for the CFL constant (for example, DG gives $\rho(A) < Ch/p^2$). Is it known how $\rho(A)$ for FD discretizations depends on stencil order or type?
CFL for high order finite difference
finite difference;cfl