Reading today about the theory of differential forms, I was left impressed how much it reminded me of second order Finite Volume Method (FVM).
I'm struggling to figure out is thinking this way just trivial or is there some deeper connection.
Well, differential forms serve to generalize some concepts deeply rooted in second order FVM, like flux of fluid trough a surface, and we are all about fluxes in FVM. Then integral theorem (of Stokes) is one of the central objects in theory of differential forms. It's proving involves an integration of differential forms on a manifold-where simplexes (triangles, tetrahedrons,etc.) appear. Manifold is actually tessellated in a same manner we represent a smooth shape over which fluid passes using straight edged cells.
These are just some of the similar things. The fact is that reading about differential forms made me not being able to stop thinking about FVM.
Does second order Finite Volume method actually represent Computational manifestation of Differential Forms theory?