Expressions of dissipated powers and stored energies in poroelastic media modeled by {u,U} and {u,P} formulations

This paper is devoted to the rigorous obtention of the energy balance in porous materials. The wave propagation in the porous media is described by Biot-Allard's {u,U} and {u,P} formulations. The paper derives the expressions for stored kinetic and strain energies together with dissipated energies. It is shown that, in the case of mixed formulations, these expressions do not correspond to the real and imaginary parts of the variational formulations. A quantitative convergence analysis of finite element scheme is then undertaken with the help of these indicators. It is shown that the order of convergence of these indicators for linear finite-element is one and that they are then well fitted to check the validity of finite-element models.