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A stabilized finite element method for the Poisson-Nernst-Planck equations in three-dimensional ion channel simulations
Wang, Qin1,2; Li, Hongliang3; Zhang, Linbo1,2; Lu, Benzhuo1,2
2021
Source PublicationAPPLIED MATHEMATICS LETTERS
ISSN0893-9659
Volume111Pages:9
AbstractThe Poisson-Nernst-Planck (PNP) model characterizing the electro-diffusion process is widely used in ion channel simulations. The standard finite element method often fails to converge, due to complicated geometries, strong fixed charges and huge bias of electric potentials or ion concentrations. We propose a novel stabilized finite element method named SUPG-IP, which inherits the upwind characteristic of the streamline-upwind/Petrov-Galerkin (SUPG) method and the smoothing effect of the interior penalty method. Numerical experiments have demonstrated that the SUPG-IP method has much better performance in positivity preserving and robustness than the standard FE and SUPG methods. Especially, the benchmark simulation of the KcsA ion channel implies that the SUPG-IP method still converges successfully under an unprecedented range of membrane potentials and ion concentrations, while the SUPG method diverges. (C) 2020 Elsevier Ltd. All rights reserved.
KeywordPoisson-Nernst-Planck Stabilized finite element method SUPG interior penalty
DOI10.1016/j.aml.2020.106652
Indexed BySCI
Language英语
Funding ProjectScience Challenge Project[TZ2016003] ; National Key Research and Development Program of China[2016YFB0201304] ; National Natural Science Foundation of China[21573274] ; National Natural Science Foundation of China[11771435]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000571465000009
PublisherPERGAMON-ELSEVIER SCIENCE LTD
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/52239
Collection中国科学院数学与系统科学研究院
Corresponding AuthorLi, Hongliang; Lu, Benzhuo
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, LSEC, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
3.Sichuan Normal Univ, Dept Math, Chengdu 610066, Peoples R China
Recommended Citation
GB/T 7714
Wang, Qin,Li, Hongliang,Zhang, Linbo,et al. A stabilized finite element method for the Poisson-Nernst-Planck equations in three-dimensional ion channel simulations[J]. APPLIED MATHEMATICS LETTERS,2021,111:9.
APA Wang, Qin,Li, Hongliang,Zhang, Linbo,&Lu, Benzhuo.(2021).A stabilized finite element method for the Poisson-Nernst-Planck equations in three-dimensional ion channel simulations.APPLIED MATHEMATICS LETTERS,111,9.
MLA Wang, Qin,et al."A stabilized finite element method for the Poisson-Nernst-Planck equations in three-dimensional ion channel simulations".APPLIED MATHEMATICS LETTERS 111(2021):9.
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