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A Two-Level Method With Backtracking For The Navier-Stokes Equations (1998)
| Venue: | SIAM J. Numer. Anal |
| Citations: | 16 - 1 self |
BibTeX
@ARTICLE{Layton98atwo-level,
author = {W. Layton and L. Tobiska and H},
title = {A Two-Level Method With Backtracking For The Navier-Stokes Equations},
journal = {SIAM J. Numer. Anal},
year = {1998},
volume = {35},
pages = {2035--2054}
}
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Abstract
. We consider a two-level method for discretization and solution of the equilibrium Navier-Stokes equations. The method yields an L 2 and H 1 optimal velocity approximation and an L 2 optimal pressure approximation. The 2-level method involves solving one small, nonlinear coarse mesh system, one Oseen problem (hence linear with positive definite symmetric part) on the fine mesh and one linear correction problem on the coarse mesh. The analysis of the method is complicated by the fact that the corrected approximation is not discretely divergence free on the fine mesh. 1. Introduction. This paper considers the finite element approximation of the steady state Navier-Stokes equations, modelling the equilibrium flow of a viscous, incompressible fluid: (1:1) 8 ? ? ! ? ? : \Gamma \Deltau + u \Delta ru+rp = f ; in\Omega ; r \Delta u = 0; in\Omega ; u = 0 on @\Omega and R pdx = 0: In (1.1),\Omega is a domain in R d ; d = 2 or 3; u :\Omega ! R d is the flow field, p :\Om...
Keyphrases
two-level method navier-stokes equation fine mesh 2-level method coarse mesh oseen problem equilibrium flow flow field nonlinear coarse mesh system finite element approximation hence linear incompressible fluid positive definite symmetric part linear correction problem gamma deltau delta equilibrium navier-stokes equation optimal pressure approximation steady state navier-stokes equation optimal velocity approximation
