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Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2018

Characterization of partial derivatives with respect to material parameters in a fluid-solid interaction problem

Izar Azpiroz
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Rabia Djellouli
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Ha Pham
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Résumé

For a fluid-solid interaction problem with Lipschitz interface, we investigate the partial Fréchet differentiability of the solutions and the approximate far-field-pattern with respect to solid material parameters. Differentiability is shown in standard Sobolev framework, and the derivatives are characterized as solutions to inhomogeneous fluid-solid transmission problems. To validate the accuracy of the characterization, we compare analytical values with numerical ones given by Interior Penalty Discontinuous Galerkin (IPDG) in a setting with circular obstacles. Our comparisons also show that IPDG gives results with high precision and incurs almost no effect of discretization error accumulation.
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Dates et versions

hal-01806939 , version 1 (06-06-2018)

Identifiants

Citer

Izar Azpiroz, Hélène Barucq, Rabia Djellouli, Ha Pham. Characterization of partial derivatives with respect to material parameters in a fluid-solid interaction problem. Journal of Mathematical Analysis and Applications, 2018, 465, pp.903--927. ⟨10.1016/j.jmaa.2018.05.046⟩. ⟨hal-01806939⟩
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