Quoted without permission from [ 2 ], 1.1 Background, bottom lines:

There has been progress on the mathematical side, which, though smaller in scale, is also significant. Apart from an unfortunate aberration period, during which it became fashionable to prove that the two-phase equations were insoluble, applied mathematicians (or, more often, engineers taking over their role) have made steady advances. They have modestly improved solution algorithms, clarified the relative merits of implicit and explicit formulations, for the most part ignored the siren voices from the "finite element" champ, and learned to accept and work within the limitations that they could not transcend.