A Nonconforming Finite Element Method for an Acoustic Fluid-Structure Interaction Problem-Reference-Cited by-同舟云学术

A Nonconforming Finite Element Method for an Acoustic Fluid-Structure Interaction Problem

Published:2017-12-08 Issue:3 Volume:18 Page:383-406
ISSN:1609-9389
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Brenner Susanne C.¹,Çeşmelioğlu Ayçıl²^ORCID,Cui Jintao³,Sung Li-Yeng¹

Affiliation:

1. Department of Mathematics & Center for Computation and Technology , Louisiana State University , Baton Rouge , LA 70803 , USA

2. Department of Mathematics & Statistics , Oakland University , Rochester , MI 48309 , USA

3. Department of Applied Mathematics , The Hong Kong Polytechnic University , Hung Hom , Hong Kong

Abstract

Abstract We study a nonconforming finite element approximation of the vibration modes of an acoustic fluid-structure interaction. Displacement variables are used for both the fluid and the solid. The numerical scheme is based on an irrotational fluid displacement formulation and hence it is free of spurious eigenmodes. The method uses weakly continuous P 1

{P_{1}}

vector fields for the fluid and classical piecewise linear elements for the solid, and it has O ⁢ ( h 2 )

{O(h^{2})}

convergence for the eigenvalues on properly graded meshes. The theoretical results are confirmed by numerical experiments.

Funder

National Science Foundation

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

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