# Why post-smoothing in MG is needed?

In pre-smoothing we eliminate high frequencies,but what about post-smoothing?Is it used for the remain high frequencies that pre-smoothing didn't eliminate?

Post-smoothing reduces the high frequency error that is introduced by the coarse grid correction. If you visualize a correction computed on a mesh of size $$2h$$, then it has no kinks on half of the nodes of the fine mesh of size $$h$$, and strong kinks on the other half. Post-smoothing distributes this a bit and leads to a coarse grid correction that doesn't show the effects of the mesh it was computed on as much.