Benchmark results for testing adaptive finite element eigenvalue procedures. II: Conforming eigenvector and eigenvalue estimates.

DOI10.1016/j.apnum.2015.12.001zbMath1334.65188OpenAlexW2206973092MaRDI QIDQ254642

Stefano Giani, Luka Grubišić, Jeffrey S. Ovall

Publication date: 8 March 2016

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2015.12.001

zbMATH Keywords

finite element methodsa posteriori error estimateseigenvalue problemseigenfunctionelliptic operatornumerical test\(hp\)-adaptivity

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) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items

\(khp\)-adaptive spectral projection based discontinuous Galerkin method for the numerical solution of wave equations with memory, Solving elliptic eigenproblems with adaptive multimesh \(hp\)-FEM

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Adaptive finite element methods for computing band gaps in photonic crystals
• An hp finite element adaptive scheme to solve the Laplace model for fluid-solid vibrations
• Benchmark results for testing adaptive finite element eigenvalue procedures
• Asymptotic analysis of high-contrast phononic crystals and a criterion for the band-gap opening
• A new \(hp\) method for the \(-\mathrm{grad}(\mathrm{div})\) operator in non-Cartesian geometries
• An adaptive strategy for \(hp\)-FEM based on testing for analyticity
• The application of the \(hp\)-finite element method to electromagnetic problems
• Perturbation theory for linear operators.
• A framework for robust eigenvalue and eigenvector error estimation and Ritz value convergence enhancement
• On weakly formulated Sylvester equations and applications
• Finite element approximation of eigenvalue problems
• On estimators for eigenvalue/eigenvector approximations
• $hp$-Finite Elements for Elliptic Eigenvalue Problems: Error Estimates Which Are Explicit with Respect to $\lambda$, h, and p
• Vibration testing for anomaly detection
• Mathematical models and reconstruction methods in magneto-acoustic imaging
• The $h{\text{ - }}p$ Version of the Finite Element Method for Domains with Curved Boundaries
• On the poisson equation with intersecting interfaces
• Eigenstructure of the Equilateral Triangle, Part I: The Dirichlet Problem
• Data Oscillation and Convergence of Adaptive FEM
• Lavrentiev regularization + Ritz approximation = uniform finite element error estimates for differential equations with rough coefficients
• An $hp$ Finite Element Method to Solve a Fluid-Solid Vibration Problem
• Error representation formula for eigenvalue approximations for positive definite operators
• On Eigenvalue and Eigenvector Estimates for Nonnegative Definite Operators
• On residual-based a posteriori error estimation in hp-FEM