A \(C^0 \mathrm{IPG}\) method and its error estimates for the Helmholtz transmission eigenvalue problem

DOI10.1016/j.cam.2017.04.024zbMath1370.65068OpenAlexW2607765999MaRDI QIDQ2012588

Hao Li, Yidu Yang, Hai Bi, JiaYu Han

Publication date: 1 August 2017

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2017.04.024

zbMATH Keywords

numerical exampleerror estimatesHelmholtzinverse scatteringtransmission eigenvaluesinterior penalty methodfourth-order problemsfourth-order eigenvalue problem\(C^0\) Lagrange elements

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46)

Related Items

Convergence of a lowest-order finite element method for the transmission eigenvalue problem ⋮ Virtual element method for the Helmholtz transmission eigenvalue problem of anisotropic media ⋮ The two-grid and multigrid discretizations of the \(C^0\)IPG method for biharmonic eigenvalue problem ⋮ Discontinuous Galerkin methods of the non-selfadjoint Steklov eigenvalue problem in inverse scattering ⋮ Finite element/holomorphic operator function method for the transmission eigenvalue problem ⋮ On trajectories of complex-valued interior transmission eigenvalues ⋮ Discontinuous Galerkin method for the interior transmission eigenvalue problem in inverse scattering theory ⋮ Nonconforming virtual element discretization for the transmission eigenvalue problem ⋮ The method of fundamental solutions for computing acoustic interior transmission eigenvalues ⋮ A \(C^1-C^0\) conforming virtual element discretization for the transmission eigenvalue problem ⋮ An adaptive \(C^0\)IPG method for the Helmholtz transmission eigenvalue problem ⋮ A lowest-order virtual element method for the Helmholtz transmission eigenvalue problem ⋮ Virtual Elements for the Transmission Eigenvalue Problem on Polytopal Meshes

Uses Software

• iFEM
• Algorithm 922

Cites Work

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