$H^2$-Conforming Methods and Two-Grid Discretizations for the Elastic Transmission Eigenvalue Problem

DOI10.4208/cicp.OA-2019-0171zbMath1473.65283OpenAlexW3082443089MaRDI QIDQ5162345

JiaYu Han, Yidu Yang, Hai Bi

Publication date: 2 November 2021

Published in: Communications in Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/cicp.oa-2019-0171

zbMATH Keywords

error estimatesfinite elementspectral elementelastic transmission eigenvalueslinear weak formulationthe two-grid discretization

Mathematics Subject Classification ID

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 (10)

Local and Parallel Finite Element Schemes for the Elastic Transmission Eigenvalue Problem ⋮ Integral Equation Method for a Non-Selfadjoint Steklov Eigenvalue Problem ⋮ A Holomorphic Operator Function Approach for the Transmission Eigenvalue Problem of Elastic Waves ⋮ Multigrid methods for the modified elastic transmission eigenvalue problem ⋮ An adaptive FEM for the elastic transmission eigenvalue problem with different elastic tensors and different mass densities ⋮ Numerical analysis of two-dimensional unsaturated soil water flow problems with two-grid finite element methods ⋮ A Simple Low-Degree Optimal Finite Element Scheme for the Elastic Transmission Eigenvalue Problem ⋮ An adaptive finite element method for the elastic transmission eigenvalue problem ⋮ The finite element method for the elastic transmission eigenvalue problem with different elastic tensors ⋮ Order Reduced Schemes for the Fourth Order Eigenvalue Problems on Multi-Connected Planar Domains

Cites Work

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• A multigrid method for Helmholtz transmission eigenvalue problems
• Error analysis for the finite element approximation of transmission eigenvalues
• Spectral element method for mixed inhomogeneous boundary value problems of fourth order
• Inverse acoustic and electromagnetic scattering theory.
• Convergence of a lowest-order finite element method for the transmission eigenvalue problem
• An \(H^m\)-conforming spectral element method on multi-dimensional domain and its application to transmission eigenvalues
• Spectral approximation to a transmission eigenvalue problem and its applications to an inverse problem
• A type of adaptive \(C^0\) non-conforming finite element method for the Helmholtz transmission eigenvalue problem
• Computation of interior elastic transmission eigenvalues using a conforming finite element and the secant method
• A C\(^{0}\)IP method of transmission eigenvalues for elastic waves
• A two-level method for nonsymmetric eigenvalue problems
• The Quadratic Eigenvalue Problem
• Mixed Methods for the Helmholtz Transmission Eigenvalues
• Inverse Scattering Theory and Transmission Eigenvalues
• Nature of the transmission eigenvalue spectrum for elastic bodies
• Two-Grid Methods for Maxwell Eigenvalue Problems
• Spectral Methods
• The Existence of an Infinite Discrete Set of Transmission Eigenvalues
• The Shifted-Inverse Iteration Based on the Multigrid Discretizations for Eigenvalue Problems
• Transmission eigenvalues and the nondestructive testing of dielectrics
• Analytical and computational methods for transmission eigenvalues
• The inverse electromagnetic scattering problem for anisotropic media
• Three-Scale Finite Element Discretizations for Quantum Eigenvalue Problems
• A New Class of Iterative Methods for Nonselfadjoint or Indefinite Problems
• Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials
• Efficient Spectral-Galerkin Method II. Direct Solvers of Second- and Fourth-Order Equations Using Chebyshev Polynomials
• A two-grid discretization scheme for eigenvalue problems
• Computing interior transmission eigenvalues for homogeneous and anisotropic media
• Computable Error Estimates for a Nonsymmetric Eigenvalue Problem
• The method of fundamental solutions for computing acoustic interior transmission eigenvalues
• Two-Sided Arnoldi and Nonsymmetric Lanczos Algorithms
• A Shifted-Inverse Adaptive Multigrid Method for the Elastic Eigenvalue Problem
• Spectral Approximation on the Unit Ball
• A computational method for the inverse transmission eigenvalue problem
• The inside–outside duality for scattering problems by inhomogeneous media
• Spectral Methods
• A multi-level correction scheme for eigenvalue problems

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