An optimal adaptive FEM for eigenvalue clusters

DOI10.1007/s00211-014-0671-8zbMath1326.65155OpenAlexW2025603126MaRDI QIDQ2350737

Dietmar Gallistl

Publication date: 25 June 2015

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-014-0671-8

zbMATH Keywords

algorithmconvergenceoptimalityadaptive methodnumerical testeigenvalue clusterfinite element method: multiple eigenvalues: Laplacian

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) 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) 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 (16)

Direct Guaranteed Lower Eigenvalue Bounds with Optimal a Priori Convergence Rates for the Bi-Laplacian ⋮ Convergence and Optimality of Higher-Order Adaptive Finite Element Methods for Eigenvalue Clusters ⋮ Convergence and quasi-optimality of adaptive finite element methods for harmonic forms ⋮ A posteriori error estimates for Maxwell's eigenvalue problem ⋮ A posteriori error analysis for nonconforming approximation of multiple eigenvalues ⋮ Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates ⋮ Guaranteed a posteriori bounds for eigenvalues and eigenvectors: Multiplicities and clusters ⋮ Optimal convergence of adaptive FEM for eigenvalue clusters in mixed form ⋮ Adaptive Finite Element Method for the Maxwell Eigenvalue Problem ⋮ An adaptive finite element scheme for the Hellinger-Reissner elasticity mixed eigenvalue problem ⋮ Asymptotically exact a posteriori error analysis for the mixed Laplace eigenvalue problem ⋮ Adaptive \(hp\)-FEM for eigenvalue computations ⋮ Rayleigh–Ritz approximation of the inf-sup constant for the divergence ⋮ A Priori Error Estimates for Finite Element Approximations to Eigenvalues and Eigenfunctions of the Laplace--Beltrami Operator ⋮ Computation of the LBB Constant for the Stokes Equation with a Least-Squares Finite Element Method ⋮ Eigenfunction behavior and adaptive finite element approximations of nonlinear eigenvalue problems in quantum physics

Cites Work

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• An oscillation-free adaptive FEM for symmetric eigenvalue problems
• Convergence and optimal complexity of adaptive finite element eigenvalue computations
• Adaptive finite element methods with convergence rates
• A framework for robust eigenvalue and eigenvector error estimation and Ritz value convergence enhancement
• Optimality of a standard adaptive finite element method
• Verified Eigenvalue Evaluation for the Laplacian over Polygonal Domains of Arbitrary Shape
• Finite element approximation of eigenvalue problems
• An Adaptive Finite Element Eigenvalue Solver of Asymptotic Quasi-Optimal Computational Complexity
• A Posteriori Error Estimates for the Finite Element Approximation of Eigenvalue Problems
• On estimators for eigenvalue/eigenvector approximations
• Convergence and quasi-optimality of adaptive FEM for Steklov eigenvalue problems
• A new error analysis for discontinuous finite element methods for linear elliptic problems
• Guaranteed lower bounds for eigenvalues
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• A Convergent Adaptive Method for Elliptic Eigenvalue Problems
• CONVERGENCE OF ADAPTIVE FINITE ELEMENT METHODS FOR EIGENVALUE PROBLEMS
• Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
• Comparison Results of Finite Element Methods for the Poisson Model Problem
• Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems
• The completion of locally refined simplicial partitions created by bisection
• Equilibrated residual error estimator for edge elements
• New A Priori FEM Error Estimates for Eigenvalues

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