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Convergent finite element discretizationsof the Navier-Stokes-Nernst-Planck-Poisson system

Published online by Cambridge University Press:  23 February 2010

Andreas Prohl  and
Markus Schmuck
Andreas Prohl
Affiliation:
Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany. prohl@na.uni-tuebingen.de
Markus Schmuck
Affiliation:
Department of Chemical Engineering, MIT Boston, 25 Ames Street, Cambridge, MA 02139, USA. schmuck@mit.edu
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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.

Keywords

Electrohydrodynamicsspace-time discretizationfinite elementsconvergence
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 44 , Issue 3 , May 2010 , pp. 531 - 571
Copyright
© EDP Sciences, SMAI, 2010

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