A 3-D HIERARCHICAL FE FORMULATION OF BIOTʹS EQUATIONS FOR ELASTO-ACOUSTIC MODELLING OF POROUS MEDIA

A three-dimensional hierarchical finite element formulation of Biotʹs equation for low frequency elasto-acoustic wave propagation in fluid saturated porous media based on a weak formulation with fluid displacement and solid displacement as dependent variables is presented. A global error measure for evaluation of the convergence is proposed. Numerical simulations of an air saturated polyurethane foam material show faster convergence for the hierarchical extensions than for linear and quadratic serendipity finite element mesh refinement extensions.