KMS Of Academy of mathematics and systems sciences, CAS
| A structure-preserving finite element discretization for the time-dependent Nernst-Planck equation | |
| Zhang, Qianru1,2; Tu, Bin3; Fang, Qiaojun3,4,5; Lu, Benzhuo1,2 | |
| 2021-06-18 | |
| Source Publication | JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
 |
| ISSN | 1598-5865 |
| Pages | 20 |
| Abstract | It is still a challenging task to get a satisfying numerical solution to the time-dependent Nernst-Planck (NP) equation, which satisfies the following three physical properties: solution nonnegativity, total mass conservation, and energy dissipation. In this work, we propose a structure-preserving finite element discretization for the time-dependent NP equation combining a reformulated Jordan-Kinderlehrer-Otto (JKO) scheme and Scharfetter-Gummel (SG) approximation. The JKO scheme transforms a partial differential equation solution problem into an optimization problem. Our finite element discretization strategy with the SG stabilization technique and the Fisher information regularization term in the reformulated JKO scheme can guarantee the convexity of the discrete objective function in the optimization problem. In this paper, we prove that our scheme can preserve discrete solution nonnegativity, maintain total mass conservation, and preserve the decay property of energy. These properties are all validated with our numerical experiments. Moreover, the later numerical results show that our scheme performs better than the traditional Galerkin method with linear Lagrangian basis functions in keeping the above physical properties even when the convection term is dominant and the grid is coarse. |
| Keyword | Structure-preserving finite element discretization Nernst-Planck equation Scharfetter-Gummel approximation Jordan-Kinderlehrer-Otto scheme |
| DOI | 10.1007/s12190-021-01571-4 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Key Research and Development Program of Ministry of Science and Technology[2016YFB0201304] ; China NSF[11771435] ; China NSF[22073110] ; Strategic Priority Research Program of the Chinese Academy of Sciences[XDB36000000] ; National Natural Science Foundation[32027801] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied ; Mathematics |
| WOS ID | WOS:000663294200001 |
| Publisher | SPRINGER HEIDELBERG |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/58843 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Tu, Bin; Lu, Benzhuo |
| Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, Natl Ctr Math & Interdisciplinary Sci, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, Beijing Key Lab Ambient Particles Hlth Effects &, Lab Theoret & Computat Nanosci,CAS Key Lab Nanoph, Natl Ctr Nanosci & Technol,CAS Ctr Excellence Nan, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, 19A Yuquan Rd, Beijing 100049, Peoples R China 5.Sino Danish Ctr Educ & Res, Beijing 101408, Peoples R China |
| Recommended Citation GB/T 7714 | Zhang, Qianru,Tu, Bin,Fang, Qiaojun,et al. A structure-preserving finite element discretization for the time-dependent Nernst-Planck equation[J]. JOURNAL OF APPLIED MATHEMATICS AND COMPUTING,2021:20. |
| APA | Zhang, Qianru,Tu, Bin,Fang, Qiaojun,&Lu, Benzhuo.(2021).A structure-preserving finite element discretization for the time-dependent Nernst-Planck equation.JOURNAL OF APPLIED MATHEMATICS AND COMPUTING,20. |
| MLA | Zhang, Qianru,et al."A structure-preserving finite element discretization for the time-dependent Nernst-Planck equation".JOURNAL OF APPLIED MATHEMATICS AND COMPUTING (2021):20. |
| Files in This Item: | There are no files associated with this item. | |||||
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment