We propose and analyse two convergent fully discrete schemes to solve the incompressible Navier-Stokes-Nernst-Planck-Poisson system. The first scheme converges to weak solutions satisfying an energy and an entropy dissipation law. The second scheme uses Chorin's projection method to obtain an efficient approximation that converges to strong solutions at optimal rates.
Mots clés : electrohydrodynamics, space-time discretization, finite elements, convergence
@article{M2AN_2010__44_3_531_0,
author = {Prohl, Andreas and Schmuck, Markus},
title = {Convergent finite element discretizations of the {Navier-Stokes-Nernst-Planck-Poisson} system},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {531--571},
publisher = {EDP-Sciences},
volume = {44},
number = {3},
year = {2010},
doi = {10.1051/m2an/2010013},
mrnumber = {2666654},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2010013/}
}
TY - JOUR AU - Prohl, Andreas AU - Schmuck, Markus TI - Convergent finite element discretizations of the Navier-Stokes-Nernst-Planck-Poisson system JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2010 SP - 531 EP - 571 VL - 44 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2010013/ DO - 10.1051/m2an/2010013 LA - en ID - M2AN_2010__44_3_531_0 ER -
%0 Journal Article %A Prohl, Andreas %A Schmuck, Markus %T Convergent finite element discretizations of the Navier-Stokes-Nernst-Planck-Poisson system %J ESAIM: Modélisation mathématique et analyse numérique %D 2010 %P 531-571 %V 44 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2010013/ %R 10.1051/m2an/2010013 %G en %F M2AN_2010__44_3_531_0
Prohl, Andreas; Schmuck, Markus. Convergent finite element discretizations of the Navier-Stokes-Nernst-Planck-Poisson system. ESAIM: Modélisation mathématique et analyse numérique, Tome 44 (2010) no. 3, pp. 531-571. doi : 10.1051/m2an/2010013. http://www.numdam.org/articles/10.1051/m2an/2010013/
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