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Concerns
editI don't believe the proposed diffuse element method (DEM) is similar, rather or otherwise, to smoothed particle hydrodynamics.
I believe moving least squares was used purely for function approximation before the proposal of the DEM. In the same way, a finite element function space on a mesh could be used for function approximation given values at the nodes; this in no way detracts from the intellectual contribution of taking this idea forward to solve ordinary and partial differential equations.
I seem to recall the main genuine criticism of the DEM was exactly that it was *imprecise* with regard to evaluation of derivatives (at least as first conceived).