An a posteriori residual error estimator for the finite element method on anisotropic tetrahedral meshes
type: Item
instance of: scholarly article
title: An a posteriori residual error estimator for the finite element method on anisotropic tetrahedral meshes
zbMATH Open document ID: 0965.65125
published in: Numerische Mathematik
publication date: 2001-08-02T00:00:00Z
review text: A new a posteriori residual error estimator is defined and analyzed for anisotropic tetrahedral finite element meshes. All considerations carry over to anisotropic triangular meshes with minor changes only. The lower error bound is obtained by means of bubble functions and the corresponding anisotropic inverse inequalities. To prove the upper error bound, it is vital that an anisotropic mesh corresponds to the anisotropic function under consideration. Making use of this correspondence anisotropic interpolation estimates and subsequently the upper error bound are proved. A numerical example confirms the theoretical analysis.
reviewed by: Zbigniew Dżygadło
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 1538608
zbMATH Keywords: finite element method
zbMATH Keywords: a posteriori residual error estimator
zbMATH Keywords: anisotropic triangular meshes
zbMATH Keywords: error bound
zbMATH Keywords: numerical example
author: Gerd Kunert
MaRDI profile type: Publication
full work available at URL: s002110000170
OpenAlex ID: W2059500686
DOI: 10.1007/S002110000170
description: scientific article; zbMATH DE number 1538608