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On some difficulties occurring in the simulation of incompressible fluid flows by domain decomposition methods. (English) Zbl 0654.76020
Domain decomposition methods for partial differential equations, 1st Int. Symp., Paris/France 1987, 313-332 (1988).
[For the entire collection see Zbl 0649.00019.]
This paper deals with the main problems encountered when applying domain decomposition methods to the solution of Navier-Stokes or Shallow Water equations. After a brief summary of the difficulties related to industrial fluid dynamics computations using the finite element method we analyze on a simplified Stokes model the theoretical formulation of the matching operator and the main obstacles raised when implementation of domain decomposition methods is considered. Those considerations lead us to inquire about the relevancy of such methods, to the industrial problems we face.

76D05 Navier-Stokes equations for incompressible viscous fluids
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M99 Basic methods in fluid mechanics