Isogeometric discretizations of the Stokes problem: stability analysis by the macroelement technique

We propose and study high-regularity isogeometric discretizations of the Stokes problem. We address the Taylor–Hood isogeometric element, already known in this context, and a new Subgrid element which allows highest regularity velocity and pressure fields. Our stability analysis grounds on a characterization of full-rank scalar products for splines, which is the key theoretical result of this paper. We include numerical testing on two- and three-dimensional benchmarks.