Domain decomposition preconditioning in the hierarchical \(p\)-version of the finite element method
type: Item
instance of: scholarly article
title: Domain decomposition preconditioning in the hierarchical \(p\)-version of the finite element method
zbMATH Open document ID: 0936.65142
DOI: 10.1016/S0168-9274(98)00077-4
author: K. Appert
published in: Applied Numerical Mathematics
publication date: 2000-05-22T00:00:00Z
review text: The \(p\)-version of the finite element method for solving linear second-order elliptic equations in an arbitrary sufficiently smooth domain is studied in the framework of the domain decomposition (DD) method. Curvilinear elements associated with the square reference elements and satisfying conditions of generalized quasiuniformity are used to approximate the boundary and the boundary conditions. Two types of square reference elements are primarily considered with the products of integrated Legendre polynomials for coordinate functions. Condition number estimates are given, and preconditioning of the problems arising on subdomains and of the Schur complement together with the derivation of the global DD preconditioner are all considered. The authors obtain several DD preconditioners for which the generalized condition numbers vary from \(O((\log p)^3)\) to \(O(1)\).
reviewed by: Michael Sever
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 1311308
zbMATH Keywords: condition number
zbMATH Keywords: \(p\)-version
zbMATH Keywords: finite element method
zbMATH Keywords: domain decomposition
zbMATH Keywords: preconditioning
describes a project that uses: symrcm
MaRDI profile type: Publication
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full work available at URL: s0168-9274(98)00077-4
OpenAlex ID: W2088438462
description: scientific article; zbMATH DE number 1311308