A structure-preserving finite element discretization for the time-dependent Nernst-Planck equation

doi:10.1007/s12190-021-01571-4

CSpace

	A structure-preserving finite element discretization for the time-dependent Nernst-Planck equation
	Zhang, Qianru 1,2; Tu, Bin 3; Fang, Qiaojun 3,4,5; Lu, Benzhuo 1,2
	2021-06-18
发表期刊	JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
ISSN	1598-5865
页码	20
摘要	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.
关键词	Structure-preserving finite element discretization Nernst-Planck equation Scharfetter-Gummel approximation Jordan-Kinderlehrer-Otto scheme
DOI	10.1007/s12190-021-01571-4
收录类别	SCI
语种	英语
资助项目	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研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000663294200001
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58843
专题	中国科学院数学与系统科学研究院
通讯作者	Tu, Bin; Lu, Benzhuo
作者单位	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
推荐引用方式 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.