  An hyperelastic biphasic model is presented. For slow-draining problems
(permeability less than 1\times10-2 mm4 N-1 s-1), numerical instabilities in
the form of non-physical oscillations in the pressure field are observed in 3D
problems using tetrahedral Taylor-Hood finite elements. As an alternative to
considerable mesh refinement, a Galerkin least-square stabilization framework
is proposed. This technique drastically reduces the pressure discrepancies and
prevents these oscillations from propagating towards the centre of the medium.
The performance and robustness of this technique are demonstrated on a 3D
numerical example.
