Atsushi Suzuki
Faculty of Mathematics, Kyushu University, Japan

An iterative substructuring solver for the Stokes equations
Iterative substructuring method with preconditioning technique is an attractive method for parallel computation of finite element equations. The balancing Neumann-Neumann preconditioner was developed for elliptic problems by J. Mandel [1993]. This method was applied to the Stokes equations with Q2/Q0 finite elements by L. F. Pavarino and O. B. Widlund [2002]. This extension to the indefinite system requires a further inf-sup condition for the coarse problem in the balancing procedure. However, the GLS-type stabilization term for P1/P1 finite elements guarantees solvability in a class of subspaces and this property makes the coarse problem in the preconditioner to be simple as same as the case of elliptic problems. The conjugate gradient algorithm for indefinite system leads to a fast implementation of the algorithm.