Title: BDDC Algorithms for Incompressible Stokes Equations


Author:  Jing Li and Olof B. Widlund

The purpose of this paper is to extend the BDDC (balancing domain
decomposition by constraints) algorithm to saddle-point problems
that arise when mixed finite element methods are used to
approximate the system of incompressible Stokes equations. The
BDDC algorithms are iterative substructuring methods, which form a
class of domain decomposition methods based on the decomposition
of the domain of the differential equations into nonoverlapping
subdomains. They are defined in terms of a set of primal
continuity constraints, which are enforced across the interface
between the subdomains and which provide a coarse space component
of the preconditioner. Sets of such constraints are identified for
which bounds on the rate of convergence can be established that
are just as strong as previously known bounds for the elliptic
case. In fact, the preconditioned operator is effectively positive
definite, which makes the use of a conjugate gradient method
possible. A close connection is also established between the BDDC
and FETI-DP algorithms for the Stokes case.