Issue |
ESAIM: M2AN
Volume 58, Number 1, January-February 2024
|
|
---|---|---|
Page(s) | 303 - 333 | |
DOI | https://doi.org/10.1051/m2an/2023103 | |
Published online | 22 February 2024 |
Low-order fictitious domain method with enhanced mass conservation for an interface stokes problem
Sorbonne Université, CNRS, Laboratoire Jacques-Louis Lions (LJLL), Inria, Paris, France
* Corresponding author: miguel.fernandez@inria.fr
Received:
27
April
2023
Accepted:
13
December
2023
One of the main difficulties that has to be faced with fictitious domain approximation of incompressible flows with immersed interfaces is related to the potential lack of mass conservation across the interfaces. In this paper, we propose and analyze a low order fictitious domain stabilized finite element method which mitigates this issue with the addition of a single velocity constraint. We provide a complete a priori numerical analysis of the method under minimal regularity assumptions. A comprehensive numerical study illustrates the capabilities of the proposed method, including comparisons with alternative fitted and unfitted mesh methods.
Mathematics Subject Classification: 65N15 / 65N30 / 65N85
Key words: Stokes problem / fictitious domain method / Lagrange multiplier / interfacial mass conservation
© The authors. Published by EDP Sciences, SMAI 2024
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