I just came across Total Variation Diminishing schemes, where it has been mentioned that for the scheme to be non-oscillating, the following criteria should be followed:
- the scheme should be monotonic preserving i.e.
- it must not create local extreme
- the value of an existing local minimum must be non-decreasing, and that of a local maximum must be non-increasing.
May someone elaborate or explain, how these are not obeyed on QUICK or Central difference (as these are only conditional TVD).