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  • $\begingroup$ Non FV schemes still are conservative. You just need to use a conservative method. For example the edge-based discretization which is commonly referred to as node-centered finite volume is actually a finite difference scheme. It maintains conservation because it still uses a flux balance. There are conservative FD, FV, and FE discretizations. $\endgroup$
    – EMP
    Commented Jul 5, 2022 at 17:30
  • $\begingroup$ My understanding is that FV methods are the subset of FD methods that are conserving. $\endgroup$
    – nicholaswogan
    Commented Jul 5, 2022 at 22:00
  • $\begingroup$ That is not correct. FD is solving the strong form, FV and FEM the weak form. $\endgroup$
    – EMP
    Commented Jul 6, 2022 at 0:30
  • 1
    $\begingroup$ Subset isn't right. But it seems like there is a Venn diagram between FV and FD. You can start with the strong form with FD, or the weak form and apply FV, and end up with the same approximation. $\endgroup$
    – nicholaswogan
    Commented Jul 6, 2022 at 6:47
  • 1
    $\begingroup$ Philip Roe left a great answer to this subquestion in scicomp.stackexchange.com/a/30277/37438 $\endgroup$
    – IPribec
    Commented Jul 6, 2022 at 8:26