A unified FETI-DP approach for incompressible Stokes equations

A unified framework of FETI-DP algorithms is proposed for solving the system of linear equations arising from the mixed finite element approximation of incompressible Stokes equations. A distinctive feature of this framework is that it allows using both continuous and discontinuous pressures in the algorithm, while previous FETI-DP methods only apply to discontinuous pressures. A preconditioned conjugate gradient method is used in the algorithm with either a lumped or a Dirichlet preconditioner, and scalable convergence rates are proved. This framework is also used to describe several previously developed FETI-DP algorithms and greatly simplifies their analysis. Numerical experiments of solving a two-dimensional incompressible Stokes problem demonstrate the performances of the discussed FETI-DP algorithms represented under the same framework.