Adaptive computation of smallest eigenvalues of self-adjoint elliptic partial differential equations

DOI10.1002/nla.733zbMath1249.65226OpenAlexW1963839729MaRDI QIDQ2889393

Volker Mehrmann, Agnieszka Miedlar

Publication date: 7 June 2012

Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nla.733

zbMATH Keywords

finite element methodnumerical exampleseigenvalue problemerror estimateKrylov subspace methodadaptive finite element methodelliptic eigenvalue problemadaptive refinement of the meshself-adjoint elliptic eigenvalue problems

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) 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) Iterative numerical methods for linear systems (65F10) 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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Uses Software

• JDQR
• ARPACK
• JDQZ
• na14

Cites Work

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• A Convergent Adaptive Method for Elliptic Eigenvalue Problems
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• New estimates for Ritz vectors
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• A Posteriori and a Priori Error Analysis for Finite Element Approximations of Self-Adjoint Elliptic Eigenvalue Problems
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• A Convergent Adaptive Algorithm for Poisson’s Equation
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• The Matrix Eigenvalue Problem
• Majorization for Changes in Angles Between Subspaces, Ritz Values, and Graph Laplacian Spectra
• New A Priori FEM Error Estimates for Eigenvalues
• A posteriori error control for finite element approximations of elliptic eigenvalue problems
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