Higher order stable generalized finite element method for the elliptic eigenvalue and source problems with an interface in 1D

DOI10.1016/j.cam.2019.112558zbMath1433.65268arXiv1810.10299OpenAlexW2982478084MaRDI QIDQ2292025

Quanling Deng, Victor Manuel Calo

Publication date: 31 January 2020

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

Full work available at URL: https://arxiv.org/abs/1810.10299

zbMATH Keywords

eigenvalue problemFEMinterface problemSGFEM

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) Second-order elliptic equations (35J15) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (4)

Construction of discontinuous enrichment functions for enriched or generalized FEM's for interface elliptic problems in 1D ⋮ High-Order Enriched Finite Element Methods for Elliptic Interface Problems with Discontinuous Solutions ⋮ On the application of stable generalized finite element method for quasilinear elliptic two-point BVP ⋮ A generalized isogeometric analysis of elliptic eigenvalue and source problems with an interface

Uses Software

• XFEM

Cites Work

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• Stable generalized finite element method (SGFEM)
• Finite element and NURBS approximations of eigenvalue, boundary-value, and initial-value problems
• \(hp\)-adaptive composite discontinuous Galerkin methods for elliptic eigenvalue problems on complicated domains
• Higher order stable generalized finite element method
• Isogeometric analysis of structural vibrations
• The partition of unity finite element method: basic theory and applications
• An extended finite element method with higher-order elements for curved cracks
• Theory and practice of finite elements.
• The design and analysis of the generalized finite element method
• Optimal spectral approximation of \(2 n\)-order differential operators by mixed isogeometric analysis
• Dispersion-minimized mass for isogeometric analysis
• Dispersion-optimized quadrature rules for isogeometric analysis: modified inner products, their dispersion properties, and optimally blended schemes
• Strongly stable generalized finite element method: application to interface problems
• Dispersion-minimizing quadrature rules for \(C^1\) quadratic isogeometric analysis
• Spectral approximation properties of isogeometric analysis with variable continuity
• Discontinuous Galerkin approximation of the Laplace eigenproblem
• Stable generalized finite element method and associated iterative schemes; application to interface problems
• Generalization of the Pythagorean eigenvalue error theorem and its application to isogeometric analysis
• Dispersion optimized quadratures for isogeometric analysis
• Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: comparison of p-method finite elements with \(k\)-method NURBS
• The extended/generalized finite element method: An overview of the method and its applications
• Optimally Blended Spectral-Finite Element Scheme for Wave Propagation and NonStandard Reduced Integration
• Eigenvalue approximations by mixed methods
• Eigenvalue Approximation by Mixed and Hybrid Methods
• Rate of Convergence Estimates for Nonselfadjoint Eigenvalue Approximations
• Spectral Approximation for Compact Operators
• Spectral approximation of elliptic operators by the Hybrid High-Order method
• Spectral approximations by the HDG method
• The Mathematical Theory of Finite Element Methods
• High-order extended finite element method for cracked domains
• The generalized finite element method

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