Indefinite overlapping Schwarz methods for time-dependent Stokes problems Original Research Article

A class of indefinite overlapping Schwarz methods is introduced and studied for time-dependent Stokes problems, discretized with either mixed finite elements or mixed spectral elements. The methods proposed are based on the solution of local time-dependent Stokes problems on overlapping subdomains and on the solution of a coarse time-dependent Stokes problem defined on the coarse subdomain mesh. The resulting preconditioner is accelerated by an appropriate Krylov space method, producing a very efficient, scalable and parallel solver.