Two-grid finite-element schemes for the transient Navier-Stokes problem
ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 5, pp. 945-980.

We semi-discretize in space a time-dependent Navier-Stokes system on a three-dimensional polyhedron by finite-elements schemes defined on two grids. In the first step, the fully non-linear problem is semi-discretized on a coarse grid, with mesh-size H. In the second step, the problem is linearized by substituting into the non-linear term, the velocity 𝐮 H computed at step one, and the linearized problem is semi-discretized on a fine grid with mesh-size h. This approach is motivated by the fact that, on a convex polyhedron and under adequate assumptions on the data, the contribution of 𝐮 H to the error analysis is measured in the L 2 norm in space and time, and thus, for the lowest-degree elements, is of the order of H 2 . Hence, an error of the order of h can be recovered at the second step, provided h=H 2 .

Classification : 76D05, 65N15, 65N30, 65N55
Mots-clés : two grids, a priori estimates, duality
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Girault, Vivette; Lions, Jacques-Louis. Two-grid finite-element schemes for the transient Navier-Stokes problem. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 5, pp. 945-980. http://www.numdam.org/item/M2AN_2001__35_5_945_0/

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