Stabilized mixed finite elements for soil dynamics problems

Geomaterials present a strong interaction between the solid skeleton and the interstitial pore fluid which has to be taken into account if accurate results are required. The resulting mixed formulation in displacements and pressures is similar to those found in Fluid and Solid Dynamics, and indeed all of them exhibit the same restrictions to the shape functions which have to fulfill either the so-called Babuska-Brezzi conditions or the much simpler Zienkiewicz-Taylor patch test. This precludes the use of the same interpolation spaces for displacements and pressures, and therefore, simple elements like linear triangles in 2D and tetrahedra in 3D are not allowed. The purpose of this paper is to describe two stabilization techniques which can be used to overcome this difficulty.