Locally mass‐conserving Taylor–Hood elements for two‐ and three‐dimensional flow

Abstract

Abstract By supplementing the pressure space for Taylor–Hood elements, elements that satisfy continuity locally are produced. These elements are shown to satisfy the Babuska–Brezzi compatibility condition by using the patch argument. Two examples are presented, one illustrating the convergence rates and the other illustrating a difficulty with a Taylor–Hood element that is overcome by the element presented here.