scholarly journals Numerical Investigations on Several Stabilized Finite Element Methods for the Stokes Eigenvalue Problem

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Pengzhan Huang ◽  
Yinnian He ◽  
Xinlong Feng
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Finite Element Methods ◽  
Integration Method ◽  
Good Stability ◽  
Stabilized Finite Element Methods ◽  
Stabilized Finite Element ◽  
Numerical Investigations ◽  
Stokes Eigenvalue Problem ◽  
Element Pair

Several stabilized finite element methods for the Stokes eigenvalue problem based on the lowest equal-order finite element pair are numerically investigated. They are penalty, regular, multiscale enrichment, and local Gauss integration method. Comparisons between them are carried out, which show that the local Gauss integration method has good stability, efficiency, and accuracy properties, and it is a favorite method among these methods for the Stokes eigenvalue problem.

scholarly journals An Efficient Algorithm with Stabilized Finite Element Method for the Stokes Eigenvalue Problem

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Zhifeng Weng ◽  
Yaoxiong Cai
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Stokes Problem ◽  
Mixed Finite Element ◽  
Computational Time ◽  
Element Space ◽  
Stabilized Finite Element ◽  
Stabilized Finite Element Method ◽  
Stokes Eigenvalue Problem ◽  
Element Pair

This paper provides a two-space stabilized mixed finite element scheme for the Stokes eigenvalue problem based on local Gauss integration. The two-space strategy contains solving one Stokes eigenvalue problem using theP1-P1finite element pair and then solving an additional Stokes problem using theP2-P2finite element pair. The postprocessing technique which increases the order of mixed finite element space by using the same mesh can accelerate the convergence rate of the eigenpair approximations. Moreover, our method can save a large amount of computational time and the corresponding convergence analysis is given. Finally, numerical results are presented to confirm the theoretical analysis.

scholarly journals Numerical Study on Several Stabilized Finite Element Methods for the Steady Incompressible Flow Problem with Damping

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Jilian Wu ◽  
Pengzhan Huang ◽  
Xinlong Feng
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Incompressible Flow ◽  
Flow Problem ◽  
Integration Method ◽  
Numerical Study ◽  
Element Space ◽  
Stabilized Finite Element Methods ◽  
Stabilized Finite Element ◽  
Incompressible Flow Problem

We discuss several stabilized finite element methods, which are penalty, regular, multiscale enrichment, and local Gauss integration method, for the steady incompressible flow problem with damping based on the lowest equal-order finite element space pair. Then we give the numerical comparisons between them in three numerical examples which show that the local Gauss integration method has good stability, efficiency, and accuracy properties and it is better than the others for the steady incompressible flow problem with damping on the whole. However, to our surprise, the regular method spends less CPU-time and has better accuracy properties by using Crout solver.

Dispersion Analysis of Stabilized Finite Element Methods for Acoustic Fluid-Structure Interaction

2000 ◽  
Author(s):  
Lonny L. Thompson ◽  
Sridhar Sankar
Keyword(s):  
Finite Element ◽  
Least Squares ◽  
Finite Element Methods ◽  
Generalized Least Squares ◽  
Dispersion Analysis ◽  
Stabilized Finite Element Methods ◽  
Stabilized Finite Element ◽  
Stabilized Methods ◽  
Plate Elements ◽  
Acoustic Fluid

Abstract The application of stabilized finite element methods to model the vibration of elastic plates coupled with an acoustic fluid medium is considered. New stabilized methods based on the Hellinger-Reissner variational principle with a generalized least-squares modification are developed which yield improvement in accuracy over the Galerkin and Galerkin Generalized Least Squares (GGLS) finite element methods for both in vacuo and acoustic fluid-loaded Reissner-Mindlin plates. Through judicious selection of design parameters this formulation provides a consistent framework for enhancing the accuracy of mixed Reissner-Mindlin plate elements. Combined with stabilization methods for the acoustic fluid, the method presents a new framework for accurate modeling of acoustic fluid-loaded structures. The technique of complex wave-number dispersion analysis is used to examine the accuracy of the discretized system in the representation of free-waves for fluid-loaded plates. The influence of different finite element approximations for the fluid-loaded plate system are examined and clarified. Improved methods are designed such that the finite element dispersion relations closely match each branch of the complex wavenumber loci for fluid-loaded plates. Comparisons of finite element dispersion relations demonstrate the superiority of the hybrid least-squares (HLS) plate elements combined with stabilized methods for the fluid over standard Galerkin methods with mixed interpolation and shear projection (MITC4) and GGLS methods.

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