Convergence analysis of an efficient spectral element method for Stokes eigenvalue problem

2020 ◽  
Vol 43 (10) ◽  
pp. 6454-6463
Author(s):  
Jun Zhang ◽  
JinRong Wang ◽  
Yong Zhou
Keyword(s):  
Eigenvalue Problem ◽  
Convergence Analysis ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Stokes Eigenvalue Problem ◽  
Element Method

Mixed Spectral-Element Method for 3-D Maxwell's Eigenvalue Problem

2015 ◽  
Vol 63 (2) ◽  
pp. 317-325 ◽  
Author(s):  
Na Liu ◽  
Luis Eduardo Tobon ◽  
Yanmin Zhao ◽  
Yifa Tang ◽  
Qing Huo Liu
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Element Method

The Spectral Element Method for the Steklov Eigenvalue Problem

2013 ◽  
Vol 853 ◽  
pp. 631-635 ◽  
Author(s):  
Yan Jun Li ◽  
Yi Du Yang ◽  
Hai Bi
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Element Method ◽  
A Priori ◽  
Spectral Element ◽  
Element Approximation ◽  
Steklov Eigenvalue ◽  
Steklov Eigenvalue Problem ◽  
Priori Error Estimates ◽  
Shaped Domain ◽  
Element Method

This paper discusses the spectral element approximation with LGL node basis for the Steklov eigenvalue problem, and analyzes the a priori error estimates. Finally, numerical experi-ments on the square and the L-shaped domain are carried out to get very accurate approximations by the spectral element method.

Mixed Spectral Element Method for 2D Maxwell's Eigenvalue Problem

2015 ◽  
Vol 17 (2) ◽  
pp. 458-486 ◽  
Author(s):  
Na Liu ◽  
Luis Tobón ◽  
Yifa Tang ◽  
Qing Huo Liu
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Higher Order ◽  
The Finite Element Method ◽  
Rigorous Analysis ◽  
Edge Element ◽  
Weak Divergence ◽  
Element Method

AbstractIt is well known that conventional edge elements in solving vector Maxwell's eigenvalue equations by the finite element method will lead to the presence of spurious zero eigenvalues. This problem has been addressed for the first order edge element by Kikuchi by the mixed element method. Inspired by this approach, this paper describes a higher order mixed spectral element method (mixed SEM) for the computation of two-dimensional vector eigenvalue problem of Maxwell's equations. It utilizes Gauss-Lobatto-Legendre (GLL) polynomials as the basis functions in the finite-element framework with a weak divergence condition. It is shown that this method can suppress all spurious zero and nonzero modes and has spectral accuracy. A rigorous analysis of the convergence of the mixed SEM is presented, based on the higher order edge element interpolation error estimates, which fully confirms the robustness of our method. Numerical results are given for homogeneous, inhomogeneous, L-shape, coaxial and dual-inner-conductor cavities to verify the merits of the proposed method.

scholarly journals The Implementation of Spectral Element Method in a CAE System for the Solution of Elasticity Problems on Hybrid Curvilinear Meshes

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Dmitriy Konovalov ◽  
Anatoly Vershinin ◽  
Konstantin Zingerman ◽  
Vladimir Levin
Keyword(s):  
Mathematical Simulation ◽  
High Performance ◽  
Spectral Element Method ◽  
New Technologies ◽  
Spectral Element ◽  
High Tech ◽  
Engineering Analysis ◽  
Elasticity Problems ◽  
Cae System ◽  
Element Method

Modern high-performance computing systems allow us to explore and implement new technologies and mathematical modeling algorithms into industrial software systems of engineering analysis. For a long time the finite element method (FEM) was considered as the basic approach to mathematical simulation of elasticity theory problems; it provided the problems solution within an engineering error. However, modern high-tech equipment allows us to implement design solutions with a high enough accuracy, which requires more sophisticated approaches within the mathematical simulation of elasticity problems in industrial packages of engineering analysis. One of such approaches is the spectral element method (SEM). The implementation of SEM in a CAE system for the solution of elasticity problems is considered. An important feature of the proposed variant of SEM implementation is a support of hybrid curvilinear meshes. The main advantages of SEM over the FEM are discussed. The shape functions for different classes of spectral elements are written. Some results of computations are given for model problems that have analytical solutions. The results show the better accuracy of SEM in comparison with FEM for the same meshes.

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