Least squares \(h\)-\(p\) spectral element method for elliptic eigenvalue problems

DOI10.1016/j.amc.2012.01.078zbMath1245.65152OpenAlexW2082348268MaRDI QIDQ440927

R. K. S. Rathore, Lokendra K. Balyan, Pravir K. Dutt

Publication date: 19 August 2012

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

Full work available at URL: https://doi.org/10.1016/j.amc.2012.01.078

zbMATH Keywords

singularitiesArnoldi methodexponential accuracystability estimates\(h\)-\(p\) spectral element methodapproximation of eigenvalues and eigenvectors

Mathematics Subject Classification ID

Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (5)

An efficient numerical technique for estimating eigenvalues of second-order non-self-adjoint Sturm-Liouville problems ⋮ Nonconforming spectral element method: a friendly introduction in one dimension and a short review in higher dimensions ⋮ Unnamed Item ⋮ Evaluation of the Spectral Finite Element Method with the Theory of Phononic Crystals ⋮ Fast and accurate calculations of fourth-order non-self-adjoint Sturm-Liouville eigenvalues for problems in physics and engineering

Cites Work

• \(h\)-\(p\) spectral element method for elliptic problems on nonsmooth domains using parallel computers
• Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices
• Stability estimates for h-p spectral element methods for general elliptic problems on curvilinear domains
• Nonconforming \(h\)-\(p\) spectral element methods for elliptic problems
• Preconditioners for spectral element methods for elliptic and parabolic problems
• Eigenvalues of the Laplacian in Two Dimensions
• Regularity of the Solution of Elliptic Problems with Piecewise Analytic Data. Part I. Boundary Value Problems for Linear Elliptic Equation of Second Order
• The $h{\text{ - }}p$ Version of the Finite Element Method for Domains with Curved Boundaries
• Regularity and Numerical Solution of Eigenvalue Problems with Piecewise Analytic Data
• Nonconforming spectral/hp element methods for elliptic systems
• Approximations and Bounds for Eigenvalues of Elliptic Operators
• Equivalent Norms for Sobolev Spaces
• Rayleigh‐Ritz‐Galerkin methods for dirichlet's problem using subspaces without boundary conditions
• The principle of minimized iterations in the solution of the matrix eigenvalue problem
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