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Numerous papers tackle the issue to formulate conservative numerical schemes to solve PDEs. For example Liu, Wang, Zou claim "local mass conservation [...] is a highly preferred property of the algorithm in practical computing."

While I do understand intuitivly a certain urge to represent this physical property even in the smallest possible parcels (hence local mass conservation) what are the concrete benefits from this? Are certain show cases that explain the benefits of local mass conservation?

Also what exactly is the benefit of employing an algorithm with local (mass) conservation in contrast to an algorithm with global (mass) conservation, especially concerning elliptic PDEs, that represents a steady state solution, like they work with in the linked paper.

don-joe
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    'What are the concrete benefits from this?' - To produce numerical results that correctly describe your model. – Matthew Cassell Nov 16 '17 at 13:41
  • In what sense "correctly"? Doesn't a result from a non-conservative method also correctly describe my model? If you make it part of your model to have some sort of conservation property (e.g. mass conservation in a physical sense) then why is global conservation not enough to correctly describe your model? – don-joe Nov 16 '17 at 14:35
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    No, a result from a non-conservative method may not accurately represent the dynamics of your problem where as a conservative scheme may. For example, when you have a shock in your model. – Matthew Cassell Nov 16 '17 at 15:28
  • how so? is there some famous example or testcase? and how is that measurable? – don-joe Nov 16 '17 at 15:39
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    The point is that the underlying PDE satisfies a conservation of mass property. So it is natural to ask that numerical schemes do as well. – Jeff Nov 17 '17 at 01:25

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