A full discretization of the time-dependent Navier-Stokes equations by a two-grid scheme
ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 1, pp. 141-174.

We study a two-grid scheme fully discrete in time and space for solving the Navier-Stokes system. In the first step, the fully non-linear problem is discretized in space on a coarse grid with mesh-size H and time step k. In the second step, the problem is discretized in space on a fine grid with mesh-size h and the same time step, and linearized around the velocity u H computed in the first step. The two-grid strategy is motivated by the fact that under suitable assumptions, the contribution of u H to the error in the non-linear term, is measured in the L 2 norm in space and time, and thus has a higher-order than if it were measured in the H 1 norm in space. We present the following results: if h=H 2 =k, then the global error of the two-grid algorithm is of the order of h, the same as would have been obtained if the non-linear problem had been solved directly on the fine grid.

DOI : 10.1051/m2an:2007056
Classification : 35Q30, 74S10, 76D05
Mots-clés : two-grid scheme, non-linear problem, incompressible flow, time and space discretizations, duality argument, “superconvergence” 
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     title = {A full discretization of the time-dependent {Navier-Stokes} equations by a two-grid scheme},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {141--174},
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Abboud, Hyam; Sayah, Toni. A full discretization of the time-dependent Navier-Stokes equations by a two-grid scheme. ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 1, pp. 141-174. doi : 10.1051/m2an:2007056. http://www.numdam.org/articles/10.1051/m2an:2007056/

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