Domain decomposition method for the \(h\)-\(p\) version finite element method

DOI10.1016/S0045-7825(97)00249-1zbMath0943.65145OpenAlexW2156024331MaRDI QIDQ1971204

Weiming Cao, Ben Qi Guo

Publication date: 22 March 2000

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0045-7825(97)00249-1

zbMATH Keywords

finite element methoditerative methodsdomain decomposition methodsPoisson equationcondition numbers\(h\)-\(p\) versionadditive Schwarz methods

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (4)

Performance of parallel preconditioners for adaptive hp FEM discretization of incompressible flows ⋮ Error estimates and adaptive finite element methods ⋮ Wavelet solvers for \(hp\)-FEM discretizations in 3D using hexahedral elements ⋮ Data structures and load balancing for parallel adaptive \(hp\) finite-element methods

Cites Work

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• Iterative substructuring methods for spectral elements: Problems in three dimensions based on numerical quadrature
• The h-p version of the finite element method. I. The basic approximation results
• The h-p version of the finite element method. II. General results and applications
• Iterative solvers by substructuring for the \(p\)-version finite element method
• A preconditioner for the \(h\)-\(p\) version of the finite element method in two dimensions
• Regularity of the solutions for elliptic problems on nonsmooth domains in ℝ³, Part I: countably normed spaces on polyhedral domains
• Two-level domain decomposition preconditioning for thep-version finite element method in three dimensions
• The problem of selecting the shape functions for ap-type finite element
• The $h{\text{ - }}p$ Version of the Finite Element Method for Domains with Curved Boundaries
• The Construction of Preconditioners for Elliptic Problems by Substructuring, IV
• Efficient Preconditioning for thep-Version Finite Element Method in Two Dimensions
• Iterative Methods by Space Decomposition and Subspace Correction
• The Chebyshev–Legendre Method: Implementing Legendre Methods on Chebyshev Points
• Schwarz Analysis of Iterative Substructuring Algorithms for Elliptic Problems in Three Dimensions
• Regularity of the solutions for elliptic problems on nonsmooth domains in ℝ³. Part II: Regularity in neighbourhoods of edges
• Additive Schwarz Methods for the h-p Version of the Finite Element Method in Two Dimensions
• An Additive Schwarz Method for the h-p Version of the Finite Element Method in Three Dimensions
• Preconditioning on Element Interfaces for the p-Version Finite Element Method and Spectral Element Method
• The Construction of Preconditioners for Elliptic Problems by Substructuring. I
• Iterative Methods for the Solution of Elliptic Problems on Regions Partitioned into Substructures
• A Polylogarithmic Bound for an Iterative Substructuring Method for Spectral Elements in Three Dimensions
• A Preconditioner Based on Domain Decomposition forh-pFinite-Element Approximation on Quasi-Uniform Meshes

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