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Originally Posted by mprinkey

FEM lacks a fundamental statement of conservation. FVM (and DG) are axiomatically conservative based on face flux integrals. FEM is defined as a minimization problem--find the solution that best reduces the Galerkin (or Least-Squares) residual of this system. For solid mechanics, that minimization statement makes a lot of sense--configuration of solid mechanical systems map nicely to variational formulations. Conservation equations, however, do not.

For simple flow physics, the