{"title":"Positivity Preserving and Mass Conservative Projection Method for the Poisson–Nernst–Planck Equation","authors":"Fenghua Tong, Yongyong Cai","doi":"10.1137/23m1581649","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 2004-2024, August 2024. <br/> Abstract. We propose and analyze a novel approach to construct structure preserving approximations for the Poisson–Nernst–Planck equations, focusing on the positivity preserving and mass conservation properties. The strategy consists of a standard time marching step with a projection (or correction) step to satisfy the desired physical constraints (positivity and mass conservation). Based on the [math] projection, we construct a second order Crank–Nicolson type finite difference scheme, which is linear (exclude the very efficient [math] projection part), positivity preserving, and mass conserving. Rigorous error estimates in the [math] norm are established, which are both second order accurate in space and time. The other choice of projection, e.g., [math] projection, is discussed. Numerical examples are presented to verify the theoretical results and demonstrate the efficiency of the proposed method.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"29 1","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Numerical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1581649","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 2004-2024, August 2024. Abstract. We propose and analyze a novel approach to construct structure preserving approximations for the Poisson–Nernst–Planck equations, focusing on the positivity preserving and mass conservation properties. The strategy consists of a standard time marching step with a projection (or correction) step to satisfy the desired physical constraints (positivity and mass conservation). Based on the [math] projection, we construct a second order Crank–Nicolson type finite difference scheme, which is linear (exclude the very efficient [math] projection part), positivity preserving, and mass conserving. Rigorous error estimates in the [math] norm are established, which are both second order accurate in space and time. The other choice of projection, e.g., [math] projection, is discussed. Numerical examples are presented to verify the theoretical results and demonstrate the efficiency of the proposed method.
期刊介绍：
SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.
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