# Are FEM or DGFEM methods based on integrals or PDEs?

I know that FVM is based on the integral form of conservation laws, and FDS is based on PDEs. What I'm confused by, is whether FEM and DGFEM formulations are based on integral or pde form of conservation laws.

I have developed FEM formulations starting from integral form of transport equations but I've also found literature on that FEM approximates PDEs, so slightly confused there.

I am also not sure about DGFEM methods, with this method again, I start from the integral form of the equations, not sure if they are also be based on PDEs.

• It depends on what you mean by "integral form". FEM and DGFEM are based on variational (or weak) forms of PDEs, so they involve both partial derivatives and integrals. (An integral equation would only involve integrals, but no derivatives.) – Christian Clason Nov 28 '15 at 10:13