Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 306, Issue -, Pages 1-18Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2015.10.053
Keywords
Finite elements; Poisson-Nernst-Planck; Stability analysis; Energy estimate
Funding
- DOE, Collaboratory on Mathematics for Mesoscopic Modeling of Materials [DE-SC0009249]
- NSF [DMS-1412005, DMS-1216938]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1412005, 1159937] Funding Source: National Science Foundation
- U.S. Department of Energy (DOE) [DE-SC0009249] Funding Source: U.S. Department of Energy (DOE)
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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. (C) 2015 Elsevier Inc. All rights reserved.
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