Equivalent formulations and numerical schemes for a class of pseudo-parabolic equations

This paper investigates three different formulations for a class of pseudo-parabolic equations. Such equations are encountered, for example, as a model for two-phase porous media flows when dynamic effects in the capillary pressure are included. We first show the equivalence of the three different formulations for the original equation. On the basis of this, we further investigate the corresponding discretization in time and give some numerical examples.