<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This paper concerns the identification of a small obstacle immersed in a Stokes flow from boundary measurements. The proposed approach is based on the Kohn-Vogelius formulation and the topological sensitivity analysis method. We derive a high order asymptotic formula describing the variation of a Kohn-Vogelius type functional with respect to the insertion of a small obstacle inside the fluid flow domain. The obtained asymptotic formula will serve as very useful tools for developing accurate and robust numerical reconstruction algorithms.</p></abstract>

This paper concerns the identification of a small obstacle immersed in a Stokes flow from boundary measurements. The proposed approach is based on the Kohn-Vogelius formulation and the topological sensitivity analysis method. We derive a high order asymptotic formula describing the variation of a Kohn-Vogelius type functional with respect to the insertion of a small obstacle inside the fluid flow domain. The obtained asymptotic formula will serve as very useful tools for developing accurate and robust numerical reconstruction algorithms.

Kohn-Vogelius formulation and high-order topological asymptotic formula for identifying small obstacles in a fluid medium

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

This paper concerns the identification of a small obstacle immersed in a Stokes flow from boundary measurements. The proposed approach is based on the...

Kohn-Vogelius formulation and high-order topological asymptotic formula for identifying small obstacles in a fluid medium

Published Online: Apr 09, 2020

Page range: 35 - 59

Received: Feb 19, 2019

Accepted: Apr 25, 2019

DOI: https://doi.org/10.2478/auom-2020-0003

Keywords
Kohn-Vogelius formulation, Topological sensitivity analysis, Stokes system, Geometric inverse problem, Calculus of variations, Asymptotic formula

© 2020 Montassar Barhoumi, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Kohn-Vogelius formulation and high-order topological asymptotic formula for identifying small obstacles in a fluid medium

Published Online: Apr 09, 2020

Page range: 35 - 59

Received: Feb 19, 2019

Accepted: Apr 25, 2019

DOI: https://doi.org/10.2478/auom-2020-0003

KeywordsKohn-Vogelius formulation, Topological sensitivity analysis, Stokes system, Geometric inverse problem, Calculus of variations, Asymptotic formula

© 2020 Montassar Barhoumi, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Kohn-Vogelius formulation, Topological sensitivity analysis, Stokes system, Geometric inverse problem, Calculus of variations, Asymptotic formula