> The more popular finite volume method in industry, can also be seen as a variational problem.
By that standard, you could interpret almost any numerical method for PDEs used in academia or industry as variational (aside from some fringe ones). By "variational" I mean methods which are designed in a variational way from the start, not can be merely interpreted variationally.
Well, it helps to see these connections. For example, realising that the lowest order DG method is finite volume lets one think about how to extend well studied finite volume properties to high order DG methods.
By that standard, you could interpret almost any numerical method for PDEs used in academia or industry as variational (aside from some fringe ones). By "variational" I mean methods which are designed in a variational way from the start, not can be merely interpreted variationally.