ENERGY BALANCES IN CVFEM AND GFEM FORMULATIONS OF CONVECTION-TYPE PROBLEMS

A physical approach, based on energy balances at element and at node levels, is utilized to derive both control volume and Galerkin finite element formulations of convection-type problems. This direct approach leads to the same systems of differential equations yielded by conventional formulations, but allows us to demonstrate that there are no differences in conservation properties between the two methods. Besides, we provide reliable physical interpretations for all the steps involved in standard mathematical procedures of discretization