Lower Bounds for Eigenvalues of the Stokes Operator

2013 ◽  
Vol 5 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Jun Hu ◽  
Yunqing Huang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Lower Bound ◽  
Lower Bounds ◽  
Stokes Operator ◽  
The Finite Element Method ◽  
Discrete Eigenvalue ◽  
Nonconforming Methods ◽  
Element Method

AbstractIn this paper, we propose a condition that can guarantee the lower bound property of the discrete eigenvalue produced by the finite element method for the Stokes operator. We check and prove this condition for four nonconforming methods and one conforming method. Hence they produce eigenvalues which are smaller than their exact counterparts.

Lower Bound of Vibration Modes Using the Node-Based Smoothed Finite Element Method (NS-FEM)

2017 ◽  
Vol 14 (04) ◽  
pp. 1750036 ◽  
Author(s):  
Guirong Liu ◽  
Meng Chen ◽  
Ming Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Lower Bound ◽  
Lower Bounds ◽  
Solid Mechanics ◽  
Wave Number ◽  
Vibration Modes ◽  
Large Wave ◽  
Smoothed Finite Element Method ◽  
Element Method

The smoothed finite element method (S-FEM) has been recently developed as an effective solver for solid mechanics problems. This paper represents an effective approach to compute the lower bounds of vibration modes or eigenvalues of elasto-dynamic problems, by making use of the important softening effects of node-based S-FEM (NS-FEM). We first use NS-FEM, FEM and the analytic approach to compute the eigenvalues of transverse free vibration in strings and membranes. It is found that eigenvalues by NS-FEM are always smaller than those by FEM and the analytic method. However, NS-FEM produces spurious unphysical modes because of overly soft behavior. A technique is then proposed to remove them by analyzing their vibration shapes (eigenvectors). It is observed that spurious modes with excessively large wave numbers, which are unrelated to the physical deflection shapes but related to the discretization density, therefore can be easily removed. The final results of NS-FEM become the lower bound of eigenvalues and the accuracy can be improved via mesh refinement. And NS-FEM solutions (softer) are more reliable, because the large wave number component can be used as an indicator, which is available in FEM (stiffer), on the quality of the numerical solutions. The proposed NS-FEM procedure offers a viable and practical computational means to effectively compute the lower bounds of eigenvalues for solid mechanics problems.

Simulation of tuning graphene plasmonic behaviors by ferroelectric domains for self-driven infrared photodetector applications

Nanoscale ◽  
2019 ◽  
Vol 11 (43) ◽  
pp. 20868-20875 ◽  
Author(s):  
Junxiong Guo ◽  
Yu Liu ◽  
Yuan Lin ◽  
Yu Tian ◽  
Jinxing Zhang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interfacial Effect ◽  
Infrared Photodetector ◽  
The Finite Element Method ◽  
Ferroelectric Domains ◽  
Element Method

We propose a graphene plasmonic infrared photodetector tuned by ferroelectric domains and investigate the interfacial effect using the finite element method.

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