Energetically stable discretizations for charge transport and electrokinetic models

Maximilian S. Metti, Jinchao Xu, Chun Liu

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


A finite element discretization using a method of lines approached is proposed for approximately solving the Poisson-Nernst-Planck (PNP) equations. This discretization scheme enforces positivity of the computed solutions, corresponding to particle density functions, and a discrete energy estimate is established that takes the same form as the energy law for the continuous PNP system. This energy estimate is extended to finite element solutions to an electrokinetic model, which couples the PNP system with the incompressible Navier-Stokes equations. Numerical experiments are conducted to validate convergence of the computed solution and verify the discrete energy estimate.

Original languageEnglish (US)
Pages (from-to)1-18
Number of pages18
JournalJournal of Computational Physics
StatePublished - Feb 1 2016

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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