Virtual element method for the Helmholtz transmission eigenvalue problem of anisotropic media

DOI10.1142/S0218202522500348zbMath1497.65216MaRDI QIDQ5045186

Liquan Mei, Ji-An Meng

Publication date: 4 November 2022

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

anisotropic mediavirtual element methodtransmission eigenvalue problem\textit{a priori} and \textit{a posteriori} error estimates

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)

Related Items (6)

The A Priori and A Posteriori Error Estimates for Modified Interior Transmission Eigenvalue Problem in Inverse Scattering ⋮ Virtual element method for the modified transmission eigenvalue problem in inverse scattering theory ⋮ The mixed discontinuous Galerkin method for transmission eigenvalues for anisotropic medium ⋮ Discontinuous Galerkin method for the interior transmission eigenvalue problem in inverse scattering theory ⋮ An adaptive FEM for the elastic transmission eigenvalue problem with different elastic tensors and different mass densities ⋮ Nonconforming virtual element discretization for the transmission eigenvalue problem

Uses Software

• iFEM

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Equivalent projectors for virtual element methods
• A multi-level method for transmission eigenvalues of anisotropic media
• Error analysis for the finite element approximation of transmission eigenvalues
• On the use of \(T\)-coercivity to study the interior transmission eigenvalue problem
• A high accuracy nonconforming finite element scheme for Helmholtz transmission eigenvalue problem
• On the interior transmission eigenvalue problem
• Nonconforming finite element methods for eigenvalue problems in linear plate theory
• The matrix domain and the spectra of a generalized difference operator
• A posteriori error estimates for a virtual element method for the Steklov eigenvalue problem
• A multilevel correction method for interior transmission eigenvalue problem
• A posteriori error estimates for the virtual element method
• A new multigrid finite element method for the transmission eigenvalue problems
• The virtual element method for eigenvalue problems with potential terms on polytopic meshes.
• An adaptive \(C^0\)IPG method for the Helmholtz transmission eigenvalue problem
• \(T\)-coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients
• A virtual element method for a biharmonic Steklov eigenvalue problem
• A \(C^0 \mathrm{IPG}\) method and its error estimates for the Helmholtz transmission eigenvalue problem
• A virtual element approximation for the pseudostress formulation of the Stokes eigenvalue problem
• Approximation of PDE eigenvalue problems involving parameter dependent matrices
• A lowest-order virtual element method for the Helmholtz transmission eigenvalue problem
• Finite elements and virtual elements on classical meshes
• Efficient methods of computing interior transmission eigenvalues for the elastic waves
• Virtual element for the buckling problem of Kirchhoff-Love plates
• A linear virtual element method for the Kirchhoff plate buckling problem
• A virtual element method for the Laplacian eigenvalue problem in mixed form
• A mixed virtual element method for the vibration problem of clamped Kirchhoff plate
• The \(p\)- and \(hp\)-versions of the virtual element method for elliptic eigenvalue problems
• A posteriori error estimation and adaptivity in \textit{hp} virtual elements
• A virtual element method for the acoustic vibration problem
• An adaptive finite element method for the transmission eigenvalue problem
• The virtual element method in 50 lines of MATLAB
• A spectral-element method for transmission eigenvalue problems
• \(C^0\)IP methods for the transmission eigenvalue problem
• Virtual Element Method for general second-order elliptic problems on polygonal meshes
• Mixed Methods for the Helmholtz Transmission Eigenvalues
• Stekloff Eigenvalues in Inverse Scattering
• Inverse Scattering Theory and Transmission Eigenvalues
• Some Remarks on Eigenvalue Approximation by Finite Elements
• Finite Element Methods for Maxwell's Transmission Eigenvalues
• Virtual Element Implementation for General Elliptic Equations
• Iterative Methods for Transmission Eigenvalues
• Analytical and computational methods for transmission eigenvalues
• Finite Element Methods for Navier-Stokes Equations
• Virtual element method for second-order elliptic eigenvalue problems
• Computing interior transmission eigenvalues for homogeneous and anisotropic media
• A virtual element method for the vibration problem of Kirchhoff plates
• A virtual element method for the transmission eigenvalue problem
• Approximation in eigenvalue problems for holomorphic fredholm operator functions I
• Approximation in eigenvalue problems for holomorphic fredholm operator functions Ii (Convergence Rate)
• Finite Element Vibration Analysis of Fluid–Solid Systems without Spurious Modes
• BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
• A residual a posteriori error estimate for the Virtual Element Method
• The Hitchhiker's Guide to the Virtual Element Method
• Numerical Methods for Electronic Structure Calculations of Materials
• The nonconforming Virtual Element Method for eigenvalue problems
• Inverse Acoustic and Electromagnetic Scattering Theory
• Residuala posteriorierror estimation for the Virtual Element Method for elliptic problems
• A virtual element method for the Steklov eigenvalue problem
• The Mathematical Theory of Finite Element Methods
• New A Priori FEM Error Estimates for Eigenvalues
• A priori and a posteriori error estimates for a virtual element spectral analysis for the elasticity equations

This page was built for publication: Virtual element method for the Helmholtz transmission eigenvalue problem of anisotropic media