A finite-element method for computing nonlinear force-free fields
type: Item
instance of: scholarly article
title: A finite-element method for computing nonlinear force-free fields
zbMATH Open document ID: 1031.85003
DOI: 10.1016/S0895-7177(01)00108-X
published in: Mathematical and Computer Modelling
publication date: 2002-06-13T00:00:00Z
review text: Motivated by a proposed iterative scheme for finding solution pairs \((\lambda,{\mathbf B})\) of \[ \operatorname {curl}{\mathbf B}=\lambda{\mathbf B}, \qquad \operatorname {div}{\mathbf B}= 0,\tag{1} \] subject to suitable boundary conditions on the boundary of a bounded, simply connected domain \(\Omega\), the authors are led to consider a linear boundary value problem associated with the transport equation \[ {\mathbf j}_0\cdot \operatorname {grad}\lambda+ \varepsilon\lambda= 0\tag{2} \] and another boundary value problem associated with the elliptic system \[ \operatorname {curl}{\mathbf B}-\operatorname {grad}p= {\mathbf j}_1, \qquad \operatorname {div}{\mathbf B}= 0,\tag{3} \] where \({\mathbf j}_0,{\mathbf j}_1\) are suitably given, \(\varepsilon\in ]0,\infty[\). After adding in a diffusion term \[ -h^r \operatorname {div}({\mathbf j}_0({\mathbf j}_0\cdot \operatorname {grad}) \lambda), \] \(r,h\in ]0,\infty[\) (as suggested by the streamline diffusion method) in the transport equation, both problems become tractible by variational methods. A corresponding finite-element method is considered, error estimates are found and numerical tests are discussed for both problems. Although, convergence of the initially suggested iterative scheme is still an open question, its applicability is finally numerically tested for a particular, explicit solution of the nonlinear system (1).
reviewed by: Rainer Picard
Mathematics Subject Classification ID: 85A30
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 78A99
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 1755403
zbMATH Keywords: Beltrami flow
zbMATH Keywords: force-free magnetic fields
zbMATH Keywords: hydromagnetics
author: Tahar Z. Boulmezaoud
author: Tahar Amari
MaRDI profile type: Publication
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full work available at URL: s0895-7177(01)00108-x
OpenAlex ID: W2060181732
description: scientific article; zbMATH DE number 1755403