Mixed finite element approximation of a degenerate elliptic problem
type: Item
instance of: scholarly article
title: Mixed finite element approximation of a degenerate elliptic problem
zbMATH Open document ID: 0837.65125
author: Paola Pietra
author: L. Donatella Marini
published in: Numerische Mathematik
publication date: 1995-10-04T00:00:00Z
review text: The authors continue their thorough study of a degenerate elliptic problem that arises in the study of the electromagnetic field in a structure with cylindrical symmetry. In their previous work a conforming finite element discretization had been used to deal numerically with a weak formulation of the problem; here a mixed finite element approach is proposed for a mixed formulation in appropriate weighted (Sobolev) spaces; the weight takes into account the singularity in the problem. The existence of a unique solution for the mixed formulation is first proven; then the second part of the paper introduces convenient finite element spaces for which appropriate interpolants are defined; finally and most importantly, optimal error bounds are obtained for the finite element approximations.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 802462
zbMATH Keywords: degenerate elliptic problem
zbMATH Keywords: electromagnetic field
zbMATH Keywords: mixed finite element
zbMATH Keywords: mixed formulation
zbMATH Keywords: singularity
zbMATH Keywords: error bounds
reviewed by: Juan Pedro Milaszewicz
MaRDI profile type: Publication
full work available at URL: s002110050142
OpenAlex ID: W2020718145
DOI: 10.1007/S002110050142
description: scientific article; zbMATH DE number 802462