ON THE INF–SUP CONDITION OF MIXED FINITE ELEMENT FORMULATIONS FOR ACOUSTIC FLUIDS-Reference-Cited by-同舟云学术

ON THE INF–SUP CONDITION OF MIXED FINITE ELEMENT FORMULATIONS FOR ACOUSTIC FLUIDS

Published:2001-07 Issue:05 Volume:11 Page:883-901
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

BAO WEIZHU¹,WANG XIAODONG²,BATHE KLAUS-JÜRGEN³

Affiliation:

1. Department of Computational Science, National University of Singapore, S17, 3 Science Drive, Singapore 117543, Singapore

2. Department of Mechanical Engineering, Polytechnic University, Brooklyn, NY 11201, USA

3. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Abstract

The objective of this paper is to present a study of the solvability, stability and optimal error bounds of certain mixed finite element formulations for acoustic fluids. An analytical proof of the stability and optimal error bounds of a set of three-field mixed finite element discretizations is given, and the interrelationship between the inf–sup condition, including the numerical inf–sup test, and the eigenvalue problem pertaining to the natural frequencies is discussed.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202501001161

Reference17 articles.

1. A mixed displacement-based finite element formulation for acoustic fluid-structure interaction

2. Finite element computation of the vibration modes of a fluid—solid system

3. On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form

4. A discourse on the stability conditions for mixed finite element formulations

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