On the selection of primal unknowns for a FETI-DP formulation of the Stokes problem in two dimensions

Selection of primal unknowns is important in convergence of FETI-DP (dual-primal finite element tearing and interconnecting) methods, which are known to be the most scalable dual iterative substructuring methods. A FETI-DP algorithm for the Stokes problem without primal pressure unknowns was developed and analyzed by Kim et al. (2010) [1]. Only the velocity unknowns at the subdomain vertices are selected to be the primal unknowns and convergence of the algorithm with a lumped preconditioner is determined by the condition number bound C(H/h)(1 + log(H/h)), where H/h is the number of elements across subdomains. In this work, primal unknowns corresponding to the averages on edges are introduced and a better condition number bound C(H/h) is proved for such a selection of primal unknowns. Numerical results are included.