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Two-grid finite-element schemes for the transient Navier-Stokes problem

Published online by Cambridge University Press:  15 April 2002

Vivette Girault  and
Jacques-Louis Lions
Vivette Girault
Affiliation:
Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, 75252 Paris Cedex 05, France.
Jacques-Louis Lions
Affiliation:
Collège de France, 75231 Paris Cedex 05, France.
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Abstract

We semi-discretize in space a time-dependent Navier-Stokes systemon a three-dimensional polyhedron by finite-elements schemesdefined on two grids. In the first step, the fully non-linearproblem is semi-discretized on a coarse grid, with mesh-size H.In the second step, the problem is linearized by substitutinginto the non-linear term, the velocity u H computed at stepone, and the linearized problem is semi-discretized on a finegrid with mesh-size h. This approach is motivated by the factthat, on a convex polyhedron and under adequate assumptions on thedata, the contribution of u H to the error analysis ismeasured in the L 2 norm in space and time, and thus, for thelowest-degree elements, is of the order of H 2. Hence, an errorof the order of h can be recovered at the second step, providedh = H 2.

Keywords

Two gridsa priori estimatesduality.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 5 , September 2001 , pp. 945 - 980
Copyright
© EDP Sciences, SMAI, 2001

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