Nonlinear Galerkin methods and mixed finite elements:
two-grid algorithms for the Navier-Stokes equations |
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Authors: | Ali Ait Ou Ammi Martine Marion |
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Institution: | (1) Departement Math\'ematiques-Informatique-Syst\`emes, Ecole Centrale de Lyon, BP 163, F-69131 Ecully, France , FR |
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Abstract: | Summary.
A nonlinear Galerkin method using mixed finite
elements is presented for the two-dimensional
incompressible Navier-Stokes equations. The
scheme is based on two finite element spaces
and for the approximation of the velocity,
defined respectively on one coarse grid with grid
size and one fine grid with grid size and
one finite element space for the approximation
of the pressure. Nonlinearity and time
dependence are both treated on the coarse space.
We prove that the difference between the new
nonlinear Galerkin method and the standard
Galerkin solution is of the order of $H^2$, both in
velocity ( and pressure norm).
We also discuss a penalized version of our algorithm
which enjoys similar properties.
Received October 5, 1993 / Revised version received November
29, 1993 |
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Keywords: | Mathematics Subject Classification (1991): 65N30 |
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