On equilibrium finite elements in three-dimensional case
type: Item
instance of: scholarly article
title: On equilibrium finite elements in three-dimensional case
zbMATH Open document ID: 0902.65055
DOI: 10.1023/A:1022421722236
published in: Applications of Mathematics
publication date: 1998-09-28T00:00:00Z
full work available at URL: https://eudml.org/doc/32978
review text: The paper introduces an interior finite element approximation of the space of solenoidal vector functions with vanishing boundary flux in a class of three-dimensional bounded domains. This space plays an important role in many problems of continuum mechanics and electromagnetism. The main theorem establishes how to characterize divergence-free functions by means of the operator curl. Its proof is based on the Fourier transform. The author shows how to generate basis functions with small supports in the space of equilibrium finite elements.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 74S05
zbMATH DE Number: 1203986
zbMATH Keywords: divergence-free functions
zbMATH Keywords: finite elements
zbMATH Keywords: internal approximation
zbMATH Keywords: stream function
zbMATH Keywords: Fourier transform
author: Sergey Korotov
reviewed by: Michal Křížek
MaRDI profile type: Publication
cites work: Finite element approximation of the Navier-Stokes equations
cites work: Internal finite element approximations in the dual variational method for second order elliptic problems with curved boundaries
cites work: Internal fe approximation of spaces of divergence-free functions in three-dimensional domains
cites work: Q3996943
cites work: Éléments finis mixtes incompressibles pour l'équation de Stokes dans \(R^ 3\).
cites work: Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations
cites work: Q5638625
OpenAlex ID: W174804361
description: scientific article; zbMATH DE number 1203986