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Journal Articles Journal of Computational and Applied Mathematics Year : 2023

A Three-player Nash game for point-wise source identification in Cauchy-Stokes problems

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Abstract

We consider linear steady Stokes flow under the action of a finite number of particles located inside the flow domain. The particles exert point-wise forces on the fluid, and are unknown in number, location and magnitude. We are interested in the determination of these point-wise forces, using only a single pair of partially available Cauchy boundary measurements. The inverse problem then couples two harsh problems : identification of point-wise sources and recovery of missing boundary data. We reformulate it as a threeplayer Nash game. The first two players aim at recovering the Dirichlet and Neumann missing data, while the third one aims at the point-forces reconstruction of the number, location and magnitude of the point-forces. To illustrate the efficiency and robustness of the proposed algorithm, we finally present several numerical experiments for different geometries and source distribution, including the case of noisy measurements.
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Dates and versions

hal-03523088 , version 1 (13-01-2022)
hal-03523088 , version 2 (13-01-2023)

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Cite

Marwa Ouni, Abderrahmane Habbal, Moez Kallel. A Three-player Nash game for point-wise source identification in Cauchy-Stokes problems. Journal of Computational and Applied Mathematics, 2023, 417, pp.23. ⟨10.1016/j.cam.2022.114613⟩. ⟨hal-03523088v2⟩
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