Indefinite overlapping Schwarz methods for time-dependent Stokes problems

A class of indefinite overlapping Schwarz methods is introduced and studied for time-dependent Stokes problems, discretized with either mixed finite e lements or mixed spectral elements. The methods proposed are based on the s olution of local lime-dependent Stokes problems on overlapping subdomains a nd on the solution of a coarse time-dependent Stokes problem defined on the coarse subdomain mesh. The resulting preconditioner is accelerated by an a ppropriate Krylov space method, producing a very efficient, scalable and pa rallel solver. (C) 2000 Elsevier Science S.A. All rights reserved.