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 and time step In the second step, the problem is discretized in space on a fine grid with mesh-size and the same time step, and linearized around the velocity computed in the first step. The two-grid strategy is motivated by the fact that under suitable assumptions, the contribution of to the error in the non-linear term, is measured in the norm in space and time, and thus has a higher-order than if it were measured in the norm in space. We present the following results: if then the global error of the two-grid algorithm is of the order of , the same as would have been obtained if the non-linear problem had been solved directly on the fine grid.
Keywords: two-grid scheme, non-linear problem, incompressible flow, time and space discretizations, duality argument, “superconvergence”
@article{M2AN_2008__42_1_141_0, author = {Abboud, Hyam and Sayah, Toni}, 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}, publisher = {EDP-Sciences}, volume = {42}, number = {1}, year = {2008}, doi = {10.1051/m2an:2007056}, mrnumber = {2387425}, zbl = {1137.76032}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2007056/} }
TY - JOUR AU - Abboud, Hyam AU - Sayah, Toni TI - A full discretization of the time-dependent Navier-Stokes equations by a two-grid scheme JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2008 SP - 141 EP - 174 VL - 42 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2007056/ DO - 10.1051/m2an:2007056 LA - en ID - M2AN_2008__42_1_141_0 ER -
%0 Journal Article %A Abboud, Hyam %A Sayah, Toni %T A full discretization of the time-dependent Navier-Stokes equations by a two-grid scheme %J ESAIM: Modélisation mathématique et analyse numérique %D 2008 %P 141-174 %V 42 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2007056/ %R 10.1051/m2an:2007056 %G en %F M2AN_2008__42_1_141_0
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, Volume 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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