{"title":"Finite element approximation of dielectrophoretic force driven flow problems","authors":"P. Gerstner, V. Heuveline","doi":"10.1051/m2an/2023031","DOIUrl":null,"url":null,"abstract":"In this paper, we propose a full discretization scheme for the instationary thermal-electro-\n\nhydrodynamic (TEHD) Boussinesq equations. These equations model the dynamics of a non-isothermal,\n\ndielectric fluid under the influence of a dielectrophoretic (DEP) force. Our scheme combines an H 1 -\n\nconformal finite element method for spatial discretization with a backward differentiation formula\n\n(BDF) for time stepping. The resulting scheme allows for a decoupled solution of the individual parts\n\nof this multi-physics system. Moreover, we derive a priori convergence rates that are of first and sec-\n\nond order in time, depending on how the individual ingredients of the BDF scheme are chosen and of\n\noptimal order in space. In doing so, special care is taken of modeling the DEP force, since its original\n\nform is a cubic term. The obtained error estimates are verified by numerical experiments.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/m2an/2023031","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we propose a full discretization scheme for the instationary thermal-electro-
hydrodynamic (TEHD) Boussinesq equations. These equations model the dynamics of a non-isothermal,
dielectric fluid under the influence of a dielectrophoretic (DEP) force. Our scheme combines an H 1 -
conformal finite element method for spatial discretization with a backward differentiation formula
(BDF) for time stepping. The resulting scheme allows for a decoupled solution of the individual parts
of this multi-physics system. Moreover, we derive a priori convergence rates that are of first and sec-
ond order in time, depending on how the individual ingredients of the BDF scheme are chosen and of
optimal order in space. In doing so, special care is taken of modeling the DEP force, since its original
form is a cubic term. The obtained error estimates are verified by numerical experiments.
期刊介绍:
M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem.
Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.