An Optimization-Based Domain Decomposition Method for the Navier--Stokes Equations

Authors:
Max D. Gunzburger;Hyesuk Kwon Lee
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2000

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Abstract

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