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A second order accuracy in time for a full discretized time-dependent Navier-Stokes equations by a two-grid scheme

Sujet: [MATH:MATH_NA] Mathematics/Numerical Analysis, [MATH:MATH_NA] Mathématiques/Analyse numérique, Keywords Two-grid scheme, Non-linear problem, Incompressible flow, Time and Space discretizations, Taylor-Hood finite element, Duality argument, superconvergence
Auteur: Abboud, Hyam, Girault, Vivette, Sayah, Toni
Résumé: We study a second-order two-grid scheme fully discrete in time and space for solving the Navier-Stokes equations. The two-grid strategy consists in discretizing, in the first step, the fully non-linear problem, in space on a coarse grid with mesh-size <i>H</i> and time step Δ<i>t</i> and, in the second step, in discretizing the linearized problem around the velocity <i>u<sub>H</sub></i> computed in the first step, in space on a fine grid with mesh-size <i>h</i> and the same time step. The two-grid method has been applied for an analysis of a first order fully-discrete in time and space algorithm and we extend the method to the second order algorithm.
Disciplines: Mathématiques
Régions: Moyen-Orient