Convergent finite element discretizations of the Navier-Stokes-Nernst-Planck-Poisson system
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 3, p. 531-571

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.

DOI : https://doi.org/10.1051/m2an/2010013
Classification:  65N30,  35L60,  35L65
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {3},
     year = {2010},
     pages = {531-571},
     doi = {10.1051/m2an/2010013},
     zbl = {pre05711746},
     mrnumber = {2666654},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2010__44_3_531_0}
}
Prohl, Andreas; Schmuck, Markus. Convergent finite element discretizations of the Navier-Stokes-Nernst-Planck-Poisson system. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 3, pp. 531-571. doi : 10.1051/m2an/2010013. http://www.numdam.org/item/M2AN_2010__44_3_531_0/

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