An optimization-based domain decomposition method for the Navier-Stokes equations

An optimization-based, nonoverlapping domain decomposition method for the s olution of the Navier-Stokes equations is presented. The crux of the method is a constrained minimization problem for which the objective functional m easures the jump in the dependent variables across the common boundaries be tween subdomains; the constraints are the Navier-Stokes equations in the su bdomains with suitably chosen boundary conditions along the interfaces. We show that solutions of the minimization problem exist and derive an optimal ity system from which these solutions may be determined. Finite element app roximations of the solutions of the optimality system are examined. The dom ain decomposition method is also reformulated as a nonlinear least-squares problem and the results of some numerical experiments are given.