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Goal-oriented error estimation for fluid-structure interaction problems. (English) Zbl 1253.74037
Summary: We present an adaptive finite element method for the numerical simulation of stationary fluid-structure interaction problems. The coupled system is given in a variational and monolithic Arbitrary Lagrangian Eulerian framework. We derive methods for goal-oriented error estimation and mesh adaptation with the dual weighted residual method. Key to applying this error estimator is the underlying canonic variational formulation of the fluid-structure interaction problem by mapping the flow problem to ALE coordinates. The developed method is applied to two and three dimensional stationary benchmark problems coupling the incompressible Navier-Stokes equations with a nonlinear hyper-elastic material law.

MSC:
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S05 Finite element methods applied to problems in solid mechanics
76F65 Direct numerical and large eddy simulation of turbulence
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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