Title: A Dual-Primal FETI Method for Incompressible Stokes Equations

Authors: Jing Li

Abstract:: In this paper, a dual-primal FETI method is developed for incompressible Stokes equation approximated by mixed finite elements with discontinuous pressures. The domain of the problem is decomposed into nonoverlapping subdomains, and the continuity of the velocity across the subdomain interface is enforced by introducing Lagrange multipliers. By a Schur complement procedure, solving the indefinite Stokes problem is reduced to solving a symmetric positive definite problem for the dual variables, i.e., the Lagrange multipliers. This dual problem is solved by a Krylov space method with a Dirichlet preconditioner. At each step of the iteration, both subdomain problems and a coarse problem on the course subdomain mesh are solved by a direct method. It is proved that the condition number of this preconditioned problem is independent of the number of subdomains and bounded from above by the product of the inverse of the inf-sup constant of the discrete problem and the square of the logarithm of the number of unknowns in the individual subdomain problems. Illustrative results are presented by solving a lid driven cavity problem.