A Galerkin least-square stabilisation technique for hyperelastic biphasic soft tissue

An hyperelastic biphasic model is presented. For slow-draining problems (permeability less than 1 × 10−2 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 stabilisation 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.