Two-grid finite-element schemes for the steady Navier-Stokes problem in polyhedra.
Girault, V., Lions, J.-L. (2001)
Portugaliae Mathematica. Nova Série
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Girault, V., Lions, J.-L. (2001)
Portugaliae Mathematica. Nova Série
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Eberhard Bänsch, Klaus Deckelnick (1999)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Xuejun Xu, C. O. Chow, S. H. Lui (2005)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In this paper, a Dirichlet-Neumann substructuring domain decomposition method is presented for a finite element approximation to the nonlinear Navier-Stokes equations. It is shown that the Dirichlet-Neumann domain decomposition sequence converges geometrically to the true solution provided the Reynolds number is sufficiently small. In this method, subdomain problems are linear. Other version where the subdomain problems are linear Stokes problems is also presented.
Didier Bresch, Jonas Koko (2006)
International Journal of Applied Mathematics and Computer Science
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We present a numerical simulation of two coupled Navier-Stokes flows, using ope-rator-split-ting and optimization-based non-overlapping domain decomposition methods. The model problem consists of two Navier-Stokes fluids coupled, through a common interface, by a nonlinear transmission condition. Numerical experiments are carried out with two coupled fluids; one with an initial linear profile and the other in rest. As expected, the transmission condition generates a recirculation within...
Gert Lube (1994)
Banach Center Publications
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In this paper, we analyze a class of stabilized finite element formulations used in computation of (i) second order elliptic boundary value problems (diffusion-convection-reaction model) and (ii) the Navier-Stokes problem (incompressible flow model). These stabilization techniques prevent numerical instabilities that might be generated by dominant convection/reaction terms in (i), (ii) or by inappropriate combinations of velocity/pressure interpolation functions in (ii). Stability and...
Christine Bernardi, Frédéric Hecht, Rüdiger Verfürth (2009)
ESAIM: Mathematical Modelling and Numerical Analysis
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We consider a variational formulation of the three-dimensional Navier–Stokes equations with mixed boundary conditions and prove that the variational problem admits a solution provided that the domain satisfies a suitable regularity assumption. Next, we propose a finite element discretization relying on the Galerkin method and establish and error estimates.