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First Order LSFEM for Fluid‐Structure Problems
Author(s) -
KayserHerold Oliver,
Matthies Hermann G.
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410201
Subject(s) - finite element method , discretization , robustness (evolution) , compressibility , mathematics , partial differential equation , galerkin method , fluid–structure interaction , positive definite matrix , simple (philosophy) , mathematical analysis , computer science , mathematical optimization , physics , eigenvalues and eigenvectors , mechanics , philosophy , gene , biochemistry , chemistry , epistemology , quantum mechanics , thermodynamics
The Least‐Squares Finite Element Method (LSFEM) is an interesting alternative to the standard variational principles, which are used to solve partial differential equations. Advantages of the LSFEM are its robustness and the resulting symmetric positive definite matrices, which allow the use of robust iterative solvers like the CG method. In this paper we consider the application of the LSFEM for Fluid‐Structure Interaction (FSI) problems. Our model uses the LSFEM for the discretisation of the instationary incompressible Navier‐Stokes equations, which is coupled with a standard Galerkin FEM model for a linear elastic structure. The results for a simple model problem agree well with results obtained by other authors with different numerical schemes. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)