Guaranteed and Robust a Posteriori Bounds for Laplace Eigenvalues and Eigenvectors: Conforming Approximations

DOI10.1137/15M1038633OpenAlexW2502050875WikidataQ60146763 ScholiaQ60146763MaRDI QIDQ5359496

Eric Cancès, Geneviève Dusson, Martin Vohralík, Benjamin Stamm, Yvon Maday

Publication date: 25 September 2017

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1038633

zbMATH Keywords

stopping criteriaconforming finite element methoda posteriori estimateLaplace eigenvalue problemguaranteed boundinexact solvereigenvalue erroreigenvector error

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) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

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Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: a unified framework ⋮ Practical Error Bounds for Properties in Plane-Wave Electronic Structure Calculations ⋮ Flux reconstructions in the Lehmann-Goerisch method for lower bounds on eigenvalues ⋮ Fully computable a posteriori error bounds for eigenfunctions ⋮ An adaptive \(hp\)-refinement strategy with inexact solvers and computable guaranteed bound on the error reduction factor ⋮ A posteriori error estimates for Maxwell's eigenvalue problem ⋮ An overview of \textit{a posteriori} error estimation and post-processing methods for nonlinear eigenvalue problems ⋮ Dispersion optimized quadratures for isogeometric analysis ⋮ Guaranteed and Robust a Posteriori Bounds for Laplace Eigenvalues and Eigenvectors: Conforming Approximations ⋮ Projection-based guaranteed \(L^2\) error bounds for finite element approximations of Laplace eigenfunctions ⋮ An a posteriori error estimator for the spectral fractional power of the Laplacian ⋮ Guaranteed a posteriori bounds for eigenvalues and eigenvectors: Multiplicities and clusters ⋮ Computation of Tight Enclosures for Laplacian Eigenvalues ⋮ Robust Adaptive $hp$ Discontinuous Galerkin Finite Element Methods for the Helmholtz Equation ⋮ Adaptive \(hp\)-FEM for eigenvalue computations ⋮ Sharp algebraic and total a posteriori error bounds for \(h\) and \(p\) finite elements via a multilevel approach. Recovering mass balance in any situation ⋮ Stable broken $H^1$ and $H(\mathrm {div})$ polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions ⋮ On the derivation of guaranteed and \(p\)-robust a posteriori error estimates for the Helmholtz equation ⋮ Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method ⋮ The Prager–Synge theorem in reconstruction based a posteriori error estimation ⋮ An Adaptive Planewave Method for Electronic Structure Calculations

Uses Software

• FreeFem++

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