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On the Differentiability of Fluid–Structure Interaction Problems with Respect to the Problem Data

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Abstract

A coupled system of stationary fluid–structure equations in an arbitrary Lagrangian–Eulerian framework is considered in this work. Existence results presented in the literature are extended to show differentiability of the solutions to a stationary fluid–structure interaction problem with respect to the given data, volume forces and boundary values, provided a small data assumption holds. Numerical experiments are used to substantiate the theoretical findings.

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  1. Institut für Angewande Mathematik, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany

    Thomas Wick

  2. Fachbereich Mathematik, Tehnische Universität Darmstadt, Dolivostr. 15, 64293, Darmstadt, Germany

    Winnifried Wollner

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Wick, T., Wollner, W. On the Differentiability of Fluid–Structure Interaction Problems with Respect to the Problem Data. J. Math. Fluid Mech. 21, 34 (2019). https://doi.org/10.1007/s00021-019-0439-0

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