Convergence and Optimality of Higher-Order Adaptive Finite Element Methods for Eigenvalue Clusters

DOI10.1137/15M1036877zbMath1346.65058arXiv1508.06265OpenAlexW2964114492MaRDI QIDQ3188303

Alan Demlow, Andrea Bonito

Publication date: 18 August 2016

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

Full work available at URL: https://arxiv.org/abs/1508.06265

zbMATH Keywords

convergencefinite element methodoptimalityadaptivitya posteriori error estimateseigenvalue problemseigenfunctionlinear elliptic problemspectral computations

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) 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 (8)

Convergence and quasi-optimality of adaptive finite element methods for harmonic forms ⋮ An a posteriori estimator of eigenvalue/eigenvector error for penalty-type discontinuous Galerkin methods ⋮ Guaranteed a posteriori bounds for eigenvalues and eigenvectors: Multiplicities and clusters ⋮ Optimal convergence of adaptive FEM for eigenvalue clusters in mixed form ⋮ Higher order composite DG approximations of Gross-Pitaevskii ground state: benchmark results and experiments ⋮ A Priori Error Estimates for Finite Element Approximations to Eigenvalues and Eigenfunctions of the Laplace--Beltrami Operator ⋮ Finite element methods: research in India over the last decade ⋮ Eigenfunction behavior and adaptive finite element approximations of nonlinear eigenvalue problems in quantum physics

Uses Software

• deal.ii

Cites Work

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• Finite Element-Galerkin Approximation of the Eigenvalues and Eigenvectors of Selfadjoint Problems
• A Convergent Adaptive Algorithm for Poisson’s Equation
• Comparison Results of Finite Element Methods for the Poisson Model Problem
• The completion of locally refined simplicial partitions created by bisection

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