Stabilized nodal‐based finite element methods for the magnetic induction problem. (18th December 2015)

• Record Type: Journal Article
• Authors: Kaya, Utku; Wacker, Benjamin; Lube, Gert
• Is Part Of: Mathematical methods in the applied sciences. Volume 39:Number 13(2016:Sep. 15)
• Page Start: 3576
• Page End: 3590
• Publication Date: 2015-12-18
• Subjects: magnetic induction problem -- nodal‐based finite element method -- stability and error estimates; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3801
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : We consider the time‐dependent magnetic induction model as a step towards the resistive magnetohydrodynamics model in incompressible media. Conforming nodal‐based finite element approximations of the induction model with inf‐sup stable finite elements for the magnetic field and the magnetic pseudo‐pressure are investigated. Based on a residual‐based stabilization technique proposed by Badia and Codina, SIAM J. Numer. Anal. 50 (2012), pp. 398–417, we consider a stabilized nodal‐based finite element method for the numerical solution. Error estimates are given for the semi‐discrete model in space. Finally, we present some examples, for example, for the magnetic flux expulsion problem, Shercliff's test case and singular solutions of the Maxwell problem. Copyright © 2015 John Wiley & Sons, Ltd.