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?
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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.
answered Jan 31, 2020 at 23:52