Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 287, Issue -, Pages 214-223Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2016.05.007
Keywords
Poisson-Nernst-Planck system; Finite difference method; Mass conservation; Ion concentration positivity; Energy decay
Categories
Funding
- Fundamental Research Funds for the Central Universities
- Program for Young Excellent Talents at Tongji University [2013KJ012]
- National Natural Science Foundation of China [11402174, 41474103, 41204082]
- Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry
- National High Technology Research and Development Program of China [2014AA06A602]
- Natural Science Foundation of Hunan Province of China [2015JJ3148]
- Mathematics and Interdisciplinary Sciences Project of Central South University
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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. (C) 2016 Elsevier Inc. All rights reserved.
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