Title: Dual-Primal FETI methods for incompressible 
Stokes and linearized Navier-Stokes equations

(NYU-CS TR2002-828)

Author: Jing Li, Courant Institute of Mathematical Sciences

In this paper, a dual-primal FETI method is developed for solving incompressible Stokes 
equations approximated by mixed finite elements with discontinuous pressures in three 
dimensions. The domain of the problem is decomposed into non-overlapping subdomains, 
and the continuity of the velocity across the subdomain interface is enforced by 
introducing Lagrange multipliers. By a Schur complement procedure, the indefinite 
Stokes problem is reduced to 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 a coarse subdomain mesh are solved by a 
direct method. It is proved that the condition number of this preconditioned dual 
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 numerical results are presented by solving lid driven 
cavity problems. This algorithm is also extended to solving linearized non-symmetric
Navier-Stokes equation.