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Numerische Mathematik

, Volume 111, Issue 4, pp 591–630 | Cite as

Convergent discretizations for the Nernst–Planck–Poisson system

  • Andreas ProhlEmail author
  • Markus Schmuck
Article

Abstract

We propose and compare two classes of convergent finite element based approximations of the nonstationary Nernst–Planck–Poisson equations, whose constructions are motivated from energy versus entropy decay properties for the limiting system. Solutions of both schemes converge to weak solutions of the limiting problem for discretization parameters tending to zero. Our main focus is to study qualitative properties for the different approaches at finite discretization scales, like conservation of mass, non-negativity, discrete maximum principle, decay of discrete energies, and entropies to study long-time asymptotics.

Mathematics Subject Classification (2000)

65N30 35L60 35L65 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität TübingenTübingenGermany

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