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On the differentiability of fluid-structure interaction problems with respect to the problem data. (English) Zbl 1418.35316
Summary: 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.

35Q35 PDEs in connection with fluid mechanics
35Q74 PDEs in connection with mechanics of deformable solids
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
deal.ii; DOpElib
Full Text: DOI
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