Adaptive finite element solution of eigenvalue problems: Balancing of discretization and iteration error

DOI10.1515/JNUM.2010.015zbMath1222.65123OpenAlexW2088865651MaRDI QIDQ3068201

A. Westenberger, Winnifried Wollner, Rolf Rannacher

Publication date: 13 January 2011

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

Full work available at URL: https://doi.org/10.1515/jnum.2010.015

zbMATH Keywords

stopping criteriaeigenvalue problemnumerical experimentsadaptive finite element methodsa posteriori error estimatorArnoldi methoddual weighted residual methodmesh adaptioniteration errorlinear elliptic partial differential operator

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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Cites Work

• Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices
• Refined iterative algorithms based on Arnoldi's process for large unsymmetric eigenproblems
• Inexact Rayleigh quotient-type methods for eigenvalue computations
• Adaptive error control for multigrid finite element methods
• Large sparse symmetric eigenvalue problems with homogeneous linear constraints: The Lanczos process with inner-outer iterations
• Adaptive Eigenvalue Computations Using Newton's Method on the Grassmann Manifold
• A‐posteriori error estimates for the finite element method
• Edge Residuals Dominate A Posteriori Error Estimates for Low Order Finite Element Methods
• An Arnoldi code for computing selected eigenvalues of sparse, real, unsymmetric matrices
• A Posteriori Control of Modeling Errors and Discretization Errors
• A Posteriori and a Priori Error Analysis for Finite Element Approximations of Self-Adjoint Elliptic Eigenvalue Problems
• Goal-oriented error control of the iterative solution of finite element equations
• A posteriori error control for finite element approximations of elliptic eigenvalue problems

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