When it comes to discretization schemes for finite volume method, the following terms can be found in literature:

  • monotone schemes
  • monotonicity preserving schemes
  • local extremum diminishing schemes
  • TVD schemes
  • NVD schemes
  • bounded schemes
  • stable schemes
  • stability preserving schemes

A single work doesn't use all of them, rendering it more difficult to understand how these terms compare.

Could you please explain the relationship between the terms? For example: are some of them synonyms, subclasses of others, equivalent provided that some other condition is met?

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    $\begingroup$ Some of the terms you've written don't have a single meaning at all: "stable", "bounded", "stability preserving". To understand the meaning of a term in a specific paper, you'll need to look at the definition given there (or in the papers it references). So as it stands it's definitely not possible to give an answer to this question. $\endgroup$ – David Ketcheson Mar 16 '18 at 14:24
  • $\begingroup$ Do you mean that, e.g., "stable" is defined in so many different ways that it make it difficult to answer the question, or that it is not defined as if I have asked what a "joyful scheme" means? All the terms in the question can be abundantly found in literature, both in books and papers. $\endgroup$ – toliveira Mar 17 '18 at 19:09
  • $\begingroup$ @ChristianClason, could you please be more specific on the reason why the question is unclear, so it can be improved it? It is unclear why the question is unclear. :-) $\endgroup$ – toliveira Mar 17 '18 at 19:24
  • $\begingroup$ If you prefer, I can split this question in many ones, comparing the term pairwise. I thought it would be more useful to keep the discussion in just one place. $\endgroup$ – toliveira Mar 17 '18 at 19:26
  • $\begingroup$ Yes, "stable" has (at least) dozens of meanings in the literature. It should be defined in the paper of interest, or that paper should provide a reference to where it is defined. Anyone who tries to answer your question would have to guess which papers you are interested in. Asking several questions to separately compare the terms pairwise doesn't solve this at all. $\endgroup$ – David Ketcheson Mar 18 '18 at 6:28