PORTUGALIAE MATHEMATICA Vol. 58, No. 1, pp. 2557 (2001) 

TwoGrid FiniteElement Schemes for The Steady NavierStokes Problem in PolyhedraV. Girault and J.L. LionsLaboratoire d'Analyse Numérique, Université Pierre et Marie Curie75252 Paris cedex 05  FRANCE Collège de France 75231 Paris cedex 05  FRANCE Abstract: We discretize a steady NavierStokes system on a threedimensional polyhedron by finiteelements schemes defined on two grids. In the first step, the fully nonlinear problem is solved on a coarse grid, with meshsize $H$. In the second step, the problem is linearized by substituting into the nonlinear term, the velocity ${\bf u}_H$ computed at step one, and the linearized problem is solved on a fine grid with meshsize $h$. This approach is motivated by the fact that the contribution of ${\bf u}_H$ to the error analysis is measured in the $L^3$ norm, and thus, for the lowestdegree elements on a Lipschitz polyhedron, is of the order of $H^{3/2}$. Hence, an error of the order of $h$ can be recovered at the second step, provided $h = H^{3/2}$. When the domain is convex, a similar result can be obtained with $h = H^2$. Both results are valid in two dimensions. Keywords: Two grids; Nonsingular solutions; Duality. Classification (MSC2000): 76D05, 65N15, 65N30, 65N55. Full text of the article:
Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.
© 2001 Sociedade Portuguesa de Matemática
