A FETI-DP Formulation for the Stokes Problem without Primal Pressure Components

A scalable FETI–DP (Dual-Primal Finite Element Tearing and Interconnecting) algorithm for the Stokes problem is developed and analyzed. Advantages of this approach are a coarse problem without primal pressure unknowns and the use of a relatively cheap lumped preconditioner. Especially in three dimensions, these advantages provide a more robust and faster FETI-DP algorithm. In three dimensions, the velocity unknowns at subdomain corners and the averages of velocity unknowns over common faces are selected as the primal unknowns in the FETI-DP formulation. A condition number bound of the form C(H/h) is established, where C is a positive constant which is independent of any mesh parameters and H/h is the number of elements across individual subdomains.