  A non-overlapping domain decomposition algorithm is proposed to solve the
linear system arising from mixed finite element approximation of incompressible
Stokes equations. A continuous finite element space for the pressure is used.
In the proposed algorithm, Lagrange multipliers are used to enforce continuity
of the velocity component across the subdomain domain boundary. The continuity
of the pressure component is enforced in the primal form, i.e., neighboring
subdomains share the same pressure degrees of freedom on the subdomain
interface and no Lagrange multipliers are needed. After eliminating all
velocity variables and the independent subdomain interior parts of the
pressures, a symmetric positive semi-definite linear system for the subdomain
boundary pressures and the Lagrange multipliers is formed and solved by a
preconditioned conjugate gradient method. A lumped preconditioner is studied
and the condition number bound of the preconditioned operator is proved to be
independent of the number of subdomains for fixed subdomain problem size.
Numerical experiments demonstrate the convergence rate of the proposed
algorithm.
