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inria-00406493, version 1

## Convergence Analysis of a Projection Semi-Implicit Coupling Scheme for Fluid-Structure Interaction Problems

Matteo Astorino () a1, Celine Grandmont () a1

N° RR-6996 (2009)

• a –  INRIA
• 1:  REO (INRIA Paris-Rocquencourt)

• INRIA – Laboratoire Jacques-Louis Lions France
• Available versions :  v1 (2009-07-23) v2 (2009-07-24) v3 (2010-12-03)
• ### Bibliographic reference

• Type of document: Research reports
• Domain: Mathematics/Numerical Analysis
• Title: Convergence Analysis of a Projection Semi-Implicit Coupling Scheme for Fluid-Structure Interaction Problems
• Abstract: In this paper, we provide a convergence analysis of a projection semi-implicit scheme for the simulation of fluid-structure systems involving an incompressible viscous fluid. The error analysis is performed on a fully discretized linear coupled problem: a finite element approximation and a semi-implicit time-stepping strategy are respectively used for space and time discretization. The fluid is described by the Stokes equations, the structure by the classical linear elastodynamics equations and all changes of geometry are neglected. We derive an error estimate in finite time and we prove that the time discretization error for the coupling scheme is at least $\sqrt{\delta t}$. Finally, some numerical experiments that confirm the theoretical analysis are presented.
• Full text language: English
• Report type: Research Report
• Publication date: 2009
• Internal note: RR-6996

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• inria-00406493, version 1
• oai:hal.inria.fr:inria-00406493
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• Submitted on: Wednesday, 22 July 2009 15:46:22
• Updated on: Thursday, 23 July 2009 14:48:03