Nonconforming Finite Element Method for the Transmission Eigenvalue Problem

DOI10.4208/aamm.2015.m1295zbMath1490.65253OpenAlexW2530124747MaRDI QIDQ5155218

Xia Ji, Yingxia Xi, Hehu Xie

Publication date: 6 October 2021

Published in: Advances in Applied Mathematics and Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/aamm.2015.m1295

zbMATH Keywords

Morley elementnonconforming finite element methodtransmission eigenvalue

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators (34L16)

Related Items

Spectral approximation based on a mixed scheme and its error estimates for transmission eigenvalue problems ⋮ Convergence of a lowest-order finite element method for the transmission eigenvalue problem ⋮ A mixed element scheme for the Helmholtz transmission eigenvalue problem for anisotropic media ⋮ A novel spectral approximation and error estimation for transmission eigenvalues in spherical domains ⋮ An efficient spectral-Galerkin approximation based on dimension reduction scheme for transmission eigenvalues in polar geometries ⋮ Discontinuous Galerkin method for the interior transmission eigenvalue problem in inverse scattering theory ⋮ Lower Bounds of Eigenvalues of the Stokes Operator by Nonconforming Finite Elements on Local Quasi-Uniform Grids ⋮ A Simple Low-Degree Optimal Finite Element Scheme for the Elastic Transmission Eigenvalue Problem ⋮ A lowest-order virtual element method for the Helmholtz transmission eigenvalue problem ⋮ A high accuracy nonconforming finite element scheme for Helmholtz transmission eigenvalue problem ⋮ Order Reduced Schemes for the Fourth Order Eigenvalue Problems on Multi-Connected Planar Domains

Uses Software

• Algorithm 922

Cites Work

• Unnamed Item
• Unnamed Item
• Error estimates of the finite element method for interior transmission problems
• A multigrid method for Helmholtz transmission eigenvalue problems
• Error analysis for the finite element approximation of transmission eigenvalues
• On spectral analysis and a novel algorithm for transmission eigenvalue problems
• A coupled BEM and FEM for the interior transmission problem in acoustics
• The interior transmission problem
• Finite element methods (Part 1)
• Nonconforming finite element methods for eigenvalue problems in linear plate theory
• Inverse acoustic and electromagnetic scattering theory.
• \(C^{0}\)-nonconforming tetrahedral and cuboid elements for the three-dimensional fourth-order elliptic problem
• On the existence of transmission eigenvalues
• A spectral-element method for transmission eigenvalue problems
• Finite Element Methods for Maxwell's Transmission Eigenvalues
• Extrapolation of Mixed Finite Element Approximations for the Maxwell Eigenvalue Problem
• Algorithm 922
• Estimation of transmission eigenvalues and the index of refraction from Cauchy data
• The Existence of an Infinite Discrete Set of Transmission Eigenvalues
• Iterative Methods for Transmission Eigenvalues
• Transmission eigenvalues and the nondestructive testing of dielectrics
• Analytical and computational methods for transmission eigenvalues
• The inverse electromagnetic scattering problem for anisotropic media
• Transmission Eigenvalues
• Finite Element-Galerkin Approximation of the Eigenvalues and Eigenvectors of Selfadjoint Problems