On the Differentiability of Fluid–Structure Interaction Problems with Respect to the Problem Data
作者： Thomas Wick , Winnifried Wollner
DOI: 10.1007/S00021-019-0439-0
关键词: Boundary values 、 Small data 、 Interaction problem 、 Mathematical analysis 、 Mathematics 、 Work (thermodynamics) 、 Volume (compression) 、 Differentiable function 、 Fluid–structure interaction 、 Mathematical physics 、 Applied mathematics 、 Condensed matter physics 、 Computational mathematics
摘要: A coupled system of stationary fluid–structure equations in an arbitrary Lagrangian–Eulerian framework is considered this work. Existence results presented the literature are extended to show differentiability solutions a interaction problem with respect given data, volume forces and boundary values, provided small data assumption holds. Numerical experiments used substantiate theoretical findings.
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sci-hub.se 参考文章(58)
Tomáš Bodnár, Giovanni P Galdi, Šárka Nečasová, Fluid-structure interaction and biomedical applications Birkhäuser , Springer. ,(2014) , 10.1007/978-3-0348-0822-4
Yuri Bazilevs, Tayfun E. Tezduyar, Kenji Takizawa, Computational Fluid-Structure Interaction: Methods and Applications ,(2013)
Giovanni P Galdi, Rolf Rannacher, None, Fundamental Trends in Fluid-Structure Interaction World Scientific. ,(2010) , 10.1142/7675
M. Schäfer, D. C. Sternel, G. Becker, P. Pironkov, Efficient Numerical Simulation and Optimization of Fluid-Structure Interaction Springer, Berlin, Heidelberg. pp. 131- 158 ,(2011) , 10.1007/978-3-642-14206-2_6
Fabio Nobile, Numerical approximation of fluid-structure interaction problems with application to haemodynamics EPFL. ,(2001) , 10.5075/EPFL-THESIS-2458
R. Rannacher, R. Becker, An Optimal Control Approach to A-Posteriori Error Estimation Cambridge University Press. ,(2001)
Luca Formaggia, Fabio Nobile, A Stability Analysis for the Arbitrary Lagrangian Eulerian Formulation with Finite Elements East-West Journal of Mathematics. ,vol. 7, pp. 105- 132 ,(1999)
S. Turek, J. Hron, M. Razzaq, H. Wobker, M. Schäfer, Numerical Benchmarking of Fluid-Structure Interaction: A Comparison of Different Discretization and Solution Approaches Springer, Berlin, Heidelberg. pp. 413- 424 ,(2011) , 10.1007/978-3-642-14206-2_15
B. Desjardins, M. J. Esteban, Existence of Weak Solutions for the Motion of Rigid Bodies in a Viscous Fluid Archive for Rational Mechanics and Analysis. ,vol. 146, pp. 59- 71 ,(1999) , 10.1007/S002050050136
F. Nobile, C. Vergara, An Effective Fluid-Structure Interaction Formulation for Vascular Dynamics by Generalized Robin Conditions SIAM Journal on Scientific Computing. ,vol. 30, pp. 731- 763 ,(2008) , 10.1137/060678439