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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Vivette Girault, François Murat, Abner Salgado (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential,...
Ben Belgacem, Faker, Brenner, Susanne C. (2001)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
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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.
Serge Nicaise, Sarah Cochez-Dhondt (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We consider a general abstract framework of a continuous elliptic problem set on a Hilbert space that is approximated by a family of (discrete) problems set on a finite-dimensional space of finite dimension not necessarily included into . We give a series of realistic conditions on an error estimator that allows to conclude that the marking strategy of bulk type leads to the geometric convergence of the adaptive algorithm. These conditions are then verified for different concrete...
Vivette Girault, Larkin Ridgway Scott (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We propose and analyze several finite-element schemes for solving a grade-two fluid model, with a tangential boundary condition, in a two-dimensional polygon. The exact problem is split into a generalized Stokes problem and a transport equation, in such a way that it always has a solution without restriction on the shape of the domain and on the size of the data. The first scheme uses divergence-free discrete velocities and a centered discretization of the transport term, whereas the...
Noor, M.Aslam (1983)
International Journal of Mathematics and Mathematical Sciences
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Si, Zhiyong, He, Yinnian (2011)
Mathematical Problems in Engineering
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F. Brezzi (1978)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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