In order to develop a specific code for homogenization of a porous medium, I need to know what kind of finite elements I should use. The basic problem is a Stokes equation in 3D, and I have read that in 2D, one should use at least a triangle with 3 vertices as nodes for the pressure, and one more in the middle of the triangle for fluid speed. Is that true, and why ? And most important for me, what about a tetrahedron ?

1) The choice of elements depends on the geometry. In 3D, you could use tetrahedron or unstructured-hexahedron

2) If the flow is incompressible, the degrees of liberty for pressure and speed should not be placed at the same location. This can be done in many ways. As, an exemple, for a tetrahedron (or an hexahedron) the DOF for speed can be located at the center of gravity of the faces, and on the vertices for the pressure.

This as to be done to avoid false pressure modes.

3) This is a lot of work, Why don't you use an existing code?