Sharp Bounds on the Smallest Eigenvalue of Finite Element Equations with Arbitrary Meshes without Regularity Assumptions

DOI10.1137/19M128034XzbMath1468.65195arXiv1908.03460OpenAlexW3103901227WikidataQ114615460 ScholiaQ114615460MaRDI QIDQ4986818

L. Kamenski

Publication date: 28 April 2021

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.03460

zbMATH Keywords

finite element methodconditioningextreme eigenvalueseigenvalue estimatessimplicial meshes

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) 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 solution of discretized equations for boundary value problems involving PDEs (65N22)

Uses Software

• Julia

Cites Work

• Mesh-dependent stability for finite element approximations of parabolic equations with mass lumping
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• Julia: A Fresh Approach to Numerical Computing
• Conditioning of finite element equations with arbitrary anisotropic meshes
• On Mesh Geometry and Stiffness Matrix Conditioning for General Finite Element Spaces
• On the Conditioning of Finite Element Equations with Highly Refined Meshes
• The Conditioning of Boundary Element Equations on Locally Refined Meshes and Preconditioning by Diagonal Scaling
• Diagonal scaling of stiffness matrices in the Galerkin boundary element method
• Stability of Explicit Runge-Kutta Methods for High Order Finite Element Approximation of Linear Parabolic Equations
• A Study on the Conditioning of Finite Element Equations with Arbitrary Anisotropic Meshes http://admin.global-sci.org/api/check/checkTitleUpper?page=1&cate_id=13ia a Density Function Approach
• Anisotropic Mesh Refinement: The Conditioning of Galerkin Boundary Element Matrices and Simple Preconditioners

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