| Issue |
ESAIM: M2AN
Volume 57, Number 3, May-June 2023
|
|
|---|---|---|
| Page(s) | 1691 - 1729 | |
| DOI | https://doi.org/10.1051/m2an/2023031 | |
| Published online | 26 May 2023 | |
Finite element approximation of dielectrophoretic force driven flow problems
1
Engineering Mathematics and Computing Lab, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
2
Heidelberg Institute for Theoretical Studies, Schloss-Wolfsbrunnenweg 35, 69118 Heidelberg, Germany
* Corresponding author: philipp.gerstner@uni-heidelberg.de
Received:
7
June
2022
Accepted:
29
March
2023
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 H1-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 second 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.
Mathematics Subject Classification: 65N12 / 65N30 / 76W05
Key words: TEHD Boussinesq / finite element method / error estimation
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.