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

作者：

Highlights：

• We give a semi-implicit finite difference method for Poisson–Nernst–Planck systems.

• We prove rigorously the mass conservation and energy decay property of the method.

• Our method is second-order convergent in space and first-order convergent in time.

• Our method can be easily extended to the case of multi-ions.

摘要

•We give a semi-implicit finite difference method for Poisson–Nernst–Planck systems.•We prove rigorously the mass conservation and energy decay property of the method.•Our method is second-order convergent in space and first-order convergent in time.•Our method can be easily extended to the case of multi-ions.

论文关键词：Poisson–Nernst–Planck system,Finite difference method,Mass conservation,Ion concentration positivity,Energy decay

论文评审过程：Received 2 June 2015, Accepted 1 May 2016, Available online 31 May 2016, Version of Record 31 May 2016.

论文官网地址：https://doi.org/10.1016/j.amc.2016.05.007