Convergent finite element discretizations of the Navier-Stokes-Nernst-Planck-Poisson system

Andreas Prohl; Markus Schmuck

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 44, Issue: 3, page 531-571
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Prohl, Andreas, and Schmuck, Markus. "Convergent finite element discretizations of the Navier-Stokes-Nernst-Planck-Poisson system." ESAIM: Mathematical Modelling and Numerical Analysis 44.3 (2010): 531-571. <http://eudml.org/doc/250795>.

@article{Prohl2010,
abstract = { 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. },
author = {Prohl, Andreas, Schmuck, Markus},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Electrohydrodynamics; space-time discretization; finite elements; convergence; electrohydrodynamics},
language = {eng},
month = {4},
number = {3},
pages = {531-571},
publisher = {EDP Sciences},
title = {Convergent finite element discretizations of the Navier-Stokes-Nernst-Planck-Poisson system},
url = {http://eudml.org/doc/250795},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Prohl, Andreas
AU - Schmuck, Markus
TI - Convergent finite element discretizations of the Navier-Stokes-Nernst-Planck-Poisson system
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/4//
PB - EDP Sciences
VL - 44
IS - 3
SP - 531
EP - 571
AB - 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.
LA - eng
KW - Electrohydrodynamics; space-time discretization; finite elements; convergence; electrohydrodynamics
UR - http://eudml.org/doc/250795
ER -

References

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