Local Conservativity?

Sadek

Dear all,

A question has been thrown in a discussion about high resolution schemes for conservation laws regarding the definition of local conservativitiy of a scheme. Finite volume methods ensure local conservativity over a control volume whereas Finite Elements are globally conservative or conservative over an element. Where is the difference stands then? Does this depend on the definition of the control volume, i.e. if one uses a cell vertex formulation or a cell centered formulation for example? Is this important in the case of steady state problems or would that concern unsteady problems particularly?

It would be very helpful if somebody can enlighten this matter by a reference, an answer or a question.

Thanks Sadek