Preconditioning high order \(H^2\) conforming finite elements on triangles
type: Item
instance of: scholarly article
title: Preconditioning high order \(H^2\) conforming finite elements on triangles
zbMATH Open document ID: 1472.65138
author: Mark Ainsworth
author: Charles Parker
published in: Numerische Mathematik
publication date: 2021-07-06T00:00:00Z
review text: The authors are concerned with the p-version of FEM approximation of some fourth order linear elliptic problems on regular triangulations. As the condition number of the stiffness matrix typically grows rapidly with the polynomial degree p and the numbers of elements, the authors develop a preconditioner which ameliorates this bleak situation. The preconditioner is based on a smart decomposition of the global finite element space into local subspaces augmented with a global lower order vertex space. The analysis of the preconditioner on a single triangular element and the implementation aspects, including the construction of the vertex basis functions, is thoroughly performed. Three classical problems, namely ; Airy stress tensor, Stokes in a cavity domain with parabolic inflow and outflow velocity profiles and the plate one on a L-shaped domain with point loading are solved in order to underline the performances of the preconditioning technique.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 76D07
Mathematics Subject Classification ID: 76M10
zbMATH DE Number: 7368938
zbMATH Keywords: fourth order elliptic problem
zbMATH Keywords: FEM
zbMATH Keywords: p-version
zbMATH Keywords: iterative preconditioner
zbMATH Keywords: Airy stress tensor problem
zbMATH Keywords: Stokes problem
zbMATH Keywords: plate problem
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
full work available at URL: s00211-021-01206-7
OpenAlex ID: W3166155954
Wikidata QID: Q114231028
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DOI: 10.1007/S00211-021-01206-7
description: scientific article; zbMATH DE number 7368938