I do understand the meanning of "conservative discretization" within the FVM/FDM framework, indeed it is well explained in this post.
Now, according to the table in this slide (pp.8), it concludes:
- FEM suffers from "Stability for conservation laws", while Discontinuous Galerkin (DG) is just fine
I interpret this statement as, FEM(Galerkin) is a non-conservative discretization, while Discontinuous Galerkin is conservative. Am I right ?
Could anybody elaborate in mathematical sense the meaning of conservative/non-conservative in FEM/DG ? ( I do have some experience with conventional FEM but not DG :-) )
Perhaps I should ask simply: Is it possible to demonstrate whether it's a conservative discretization based upon any weak formulation(from conventional FEM/SUPG/DG)?