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Mathematical and Numerical Analysis of Some FSI Problems

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Book cover Fluid-Structure Interaction and Biomedical Applications

Part of the book series: Advances in Mathematical Fluid Mechanics ((AMFM))

Abstract

In this chapter we deal with some specific existence and numerical results applied to a 2D/1D fluid–structure coupled model, for an incompressible fluid and a thin elastic structure. We will try to underline some of the mathematical and numerical difficulties that one may face when studying this kind of problems such as the geometrical nonlinearities or the added mass effect. In particular we will point out the link between the strategies of proof of weak or strong solutions and the possible algorithms to discretize these type of coupled problems.

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Acknowledgements

Céline Grandmont was supported by the grant ANR-08-JCJC-013-01 (M3RS project) of the French Research National Agency and by REO Project, Inria Paris Rocquencourt, Inria, France & LJLL, UPMC Univeristy, Paris, France, Mária Lukáčová-Medvid’ová was supported by the German Science Foundation under the grant LU 1470/2-2,3, and Šárka Nečasová was supported by the Grant Agency of the Czech Republic n. P 201/11/1304 and by RVO 67985840.

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  1. INRIA Paris-Rocquencourt, Paris, France

    Céline Grandmont

  2. Institut für Mathematik, Johannes Gutenberg Universität Mainz, Mainz, Germany

    Mária Lukáčová-Medvid’ová

  3. Institute of Mathematics, Academy of Sciences of the Czech Republic, Prague, Czech Republic

    Šárka Nečasová

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  1. Céline Grandmont
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  1. Department of Technical Mathematics, Czech Technical University in Prague, Prague, Czech Republic

    Tomáš Bodnár

  2. Swanson School of Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania, USA

    Giovanni P. Galdi

  3. Institute of Mathematics, Academy of Sciences of the Czech Republic, Prague 1, Czech Republic

    Šárka Nečasová

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Grandmont, C., Lukáčová-Medvid’ová, M., Nečasová, Š. (2014). Mathematical and Numerical Analysis of Some FSI Problems. In: Bodnár, T., Galdi, G., Nečasová, Š. (eds) Fluid-Structure Interaction and Biomedical Applications. Advances in Mathematical Fluid Mechanics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0822-4_1

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