In this paper we solve the time-dependent incompressible Navier-Stokes equations by splitting the non-linearity and incompressibility, and using discontinuous or continuous finite element methods in space. We prove optimal error estimates for the velocity and suboptimal estimates for the pressure. We present some numerical experiments.
@article{M2AN_2005__39_6_1115_0,
author = {Girault, Vivette and Rivi\`ere, B\'eatrice and Wheeler, Mary F.},
title = {A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {39},
year = {2005},
pages = {1115-1147},
doi = {10.1051/m2an:2005048},
mrnumber = {2195907},
zbl = {1085.76037},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2005__39_6_1115_0}
}
Girault, Vivette; Rivière, Béatrice; Wheeler, Mary F. A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 39 (2005) pp. 1115-1147. doi : 10.1051/m2an:2005048. http://gdmltest.u-ga.fr/item/M2AN_2005__39_6_1115_0/
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