Bounds for eigenvalues and condition numbers in the 𝑝-version of the finite element method

DOI10.1090/S0025-5718-98-00983-1zbMath0907.65112OpenAlexW2061253771MaRDI QIDQ4210951

Ning Hu, Xian-Zhong Guo, I. Norman Katz

Publication date: 10 September 1998

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-98-00983-1

zbMATH Keywords

numerical exampleseigenvaluescondition numberstiffness matrix\(p\)-version of the finite element method

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical computation of matrix norms, conditioning, scaling (65F35)

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Cites Work

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• The h-p version of the boundary element method with geometric mesh on polygonal domains
• The p- and h-p versions of the finite element method. An overview
• Bounds on spectral condition numbers of matrices arising in the \(p\)- version of the finite element method
• Condition number and diagonal preconditioning: Comparison of the \(p\)-version and the spectral element methods
• The problem of selecting the shape functions for ap-type finite element
• A New Convergence Proof for the Multigrid Method Including the V-Cycle
• The Optimal Convergence Rate of the p-Version of the Finite Element Method
• New Convergence Estimates for Multigrid Algorithms
• An Optimal Order Process for Solving Finite Element Equations
• Thep-Version of the Finite Element Method
• Efficient Preconditioning for thep-Version Finite Element Method in Two Dimensions
• Regularity and Numerical Solution of Eigenvalue Problems with Piecewise Analytic Data
• A note on an inequality of E. Schmidt

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