An iterative adaptive finite element method for elliptic eigenvalue problems

DOI10.1016/j.cam.2012.05.002zbMath1259.65167OpenAlexW2048755574MaRDI QIDQ448407

Stefano Giani, Pavel Šolín

Publication date: 6 September 2012

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2012.05.002

zbMATH Keywords

algorithmfinite element methodnumerical exampleseigenvalue problemLaplace operatorNewton methodmesh refinementPicard methodelliptic partial differential equation

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) 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)

Related Items (7)

An adaptive algorithm based on the shifted inverse iteration for the Steklov eigenvalue problem ⋮ Solving biharmonic eigenvalue problem with Navier boundary condition via Poisson solvers on non-convex domains ⋮ A posteriori error analysis for nonconforming approximation of multiple eigenvalues ⋮ \(khp\)-adaptive spectral projection based discontinuous Galerkin method for the numerical solution of wave equations with memory ⋮ Guaranteed and Robust a Posteriori Bounds for Laplace Eigenvalues and Eigenvectors: Conforming Approximations ⋮ Adaptive Finite Element Method for the Maxwell Eigenvalue Problem ⋮ Solving elliptic eigenproblems with adaptive multimesh \(hp\)-FEM

Uses Software

• ARPACK

Cites Work

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• Adaptive finite element methods for computing band gaps in photonic crystals
• Monolithic discretization of linear thermoelasticity problems via adaptive multimesh \(hp\)-FEM
• On estimators for eigenvalue/eigenvector approximations
• Adaptive Discontinuous Galerkin Methods for Eigenvalue Problems Arising in Incompressible Fluid Flows
• A Convergent Adaptive Method for Elliptic Eigenvalue Problems
• Finite Element-Galerkin Approximation of the Eigenvalues and Eigenvectors of Selfadjoint Problems
• ARPACK Users' Guide
• Iterative Procedures for Nonlinear Integral Equations

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