Fortin operator and discrete compactness for edge elements
type: Item
instance of: scholarly article
title: Fortin operator and discrete compactness for edge elements
zbMATH Open document ID: 0967.65106
author: Daniele Boffi
published in: Numerische Mathematik
publication date: 2001-08-21T00:00:00Z
review text: A Fortin operator is constructed for tetrahedral edge elements of any order in the case of polyhedral domains. The construction is also valid for more general domains with convenient regularity hypotheses, which are satisfied by polyhedral domains. Although Fortin operators for edge elements have been introduced by other authors, they usually place restrictions such as quasiuniformity of the mesh or stronger regularity hypotheses, in order to be able to prove convergence of the operator to the identity. As a matter of fact, the main result in the paper gives a uniform estimate in the approximation of the identity in the \(L^2\) norm that depends only on the size of the mesh. This is proved after thoroughly discussing the main differences and similarities of edge and face elements in three dimensions, taking into account that edge elements are suitable for problems involving the curl operator. A final section deals with the application of the Fortin operator presented in the paper to numerically solve general Maxwell eigenvalue problems. For them it is proved by applying the main result, that the Fortin operator in this paper cannot produce spurious solutions.
reviewed by: Juan Pedro Milaszewicz
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N25
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 78M10
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 1552920
zbMATH Keywords: edge elements
zbMATH Keywords: Fortin operator
zbMATH Keywords: uniform estimates
zbMATH Keywords: polyhedral domains
zbMATH Keywords: curl operator
zbMATH Keywords: finite element method
zbMATH Keywords: convergence
zbMATH Keywords: Maxwell eigenvalue problems
zbMATH Keywords: spurious solutions
MaRDI profile type: Publication
full work available at URL: s002110000182
OpenAlex ID: W2053671897
DOI: 10.1007/S002110000182
description: scientific article; zbMATH DE number 1552920