Optimal finite element mesh for elliptic equation of divergence form

DOI10.1016/j.amc.2004.01.009zbMath1069.65134OpenAlexW2034869634MaRDI QIDQ1765839

Seungtaik Oh, Jin-Whan Yim

Publication date: 23 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.amc.2004.01.009

zbMATH Keywords

Dirichlet problemnumerical examplesmesh generationPoisson equationstiffness matrixtriangular meshesoptimal meshlinear finite elementscoercive elliptic equationoptimal condition number

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) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Cites Work

• 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
• Bounds on the spectral and maximum norms of the finite element stiffness, flexibility and mass matrices
• Efficient Preconditioning for thep-Version Finite Element Method in Two Dimensions
• On the Conditioning of Finite Element Equations with Highly Refined Meshes
• Bounds for eigenvalues and condition numbers in the 𝑝-version of the finite element method
• On Preconditioning for Finite Element Equations on Irregular Grids
• Condition of finite element matrices generated from nonuniform meshes.
• An adaptive algorithm for quasioptimal mesh generation
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item