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

Andreas Prohl; Markus Schmuck

doi:10.1051/m2an/2010013

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

Andreas Prohl
, Markus Schmuck

Research output: Contribution to journal › Article › peer-review

44 Citations (Scopus)

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.

Original language	English
Pages (from-to)	531-571
Number of pages	41
Journal	Mathematical Modelling and Numerical Analysis
Volume	44
Issue number	03
DOIs	https://doi.org/10.1051/m2an/2010013
Publication status	Published - May 2010

Keywords

Electrohydrodynamics
Space-time discretization
Finite elements
Convergence analysis

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Cite this

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title = "Convergent finite element discretizations of the Navier-Stokes-Nernst-Planck-Poisson system",

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{\textquoteright}s projection method to obtain an eﬃcient approximation that converges to strong solutions at optimal rates.",

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author = "Andreas Prohl and Markus Schmuck",

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T1 - Convergent finite element discretizations of the Navier-Stokes-Nernst-Planck-Poisson system

AU - Prohl, Andreas

AU - Schmuck, Markus

PY - 2010/5

Y1 - 2010/5

N2 - 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.

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.

KW - Electrohydrodynamics

KW - Space-time discretization

KW - Finite elements

KW - Convergence analysis

U2 - 10.1051/m2an/2010013

DO - 10.1051/m2an/2010013

M3 - Article

SN - 0764-583X

VL - 44

SP - 531

EP - 571

JO - Mathematical Modelling and Numerical Analysis

JF - Mathematical Modelling and Numerical Analysis

IS - 03

ER -

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

Abstract

Keywords

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