An energy preserving finite difference scheme for the Poisson–Nernst–Planck system

Dongdong He and Kejia Pan

Applied Mathematics and Computation, 2016, vol. 287-288, 214-223

Abstract: In this paper, we construct a semi-implicit finite difference method for the time dependent Poisson–Nernst–Planck system. Although the Poisson–Nernst–Planck system is a nonlinear system, the numerical method presented in this paper only needs to solve a linear system at each time step, which can be done very efficiently. The rigorous proof for the mass conservation and electric potential energy decay are shown. Moreover, mesh refinement analysis shows that the method is second order convergent in space and first order convergent in time. Finally we point out that our method can be easily extended to the case of multi-ions.

Keywords: Poisson–Nernst–Planck system; Finite difference method; Mass conservation; Ion concentration positivity; Energy decay (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:287-288:y:2016:i::p:214-223

DOI: 10.1016/j.amc.2016.05.007

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