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

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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Correspondence to 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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Mathematics Subject Classification

  • Primary 74F10
  • Secondary 35Q35

Keywords

  • Fluid–structure interactions
  • Differentiability of solutions with respect to problem data