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

Izar Azpiroz 1 Hélène Barucq 1 Rabia Djellouli 2 Ha Pham 1
1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
Abstract : 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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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, Elsevier, 2018, 465, pp.903--927. ⟨10.1016/j.jmaa.2018.05.046⟩. ⟨hal-01806939⟩

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