The pressure-wired Stokes element: a mesh-robust version of the Scott-Vogelius element (Q6631360)

The authors consider the numerical solution of the stationary Stokes equation in a bounded two-dimensional polygonal Lipschitz domain by a conforming Galerkin finite element method. The paper is outlined as follows. The Section 1 is an Introduction. After introducing the Stokes problem on the continuous as well as on the discrete level and the relevant notation in Section 2, the conforming pressure-wired Stokes element is defined in Section 3. The first main result in Section 4 establishes the discrete inf-sup condition for this new element with a lower bound on the inf-sup constant that is independent of \(h\), \(k\), and (nearly) critical points. The second main result controls the \(L^2\) norm of the divergence of the discrete velocity in Section. 5 and verifies its negligibility for small \(\eta \ll 1\). In Section 6 are reported numerical experiments of the convergence rates for the pressure-wired Stokes elements.