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Streamline diffusion finite element method for stationary incompressible magnetohydrodynamics
Author(s) -
Zhang GuoDong,
He Yinnian,
Zhang Yan
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21882
Subject(s) - finite element method , magnetohydrodynamics , compressibility , mathematics , convergence (economics) , partial differential equation , mixed finite element method , diffusion , mathematical analysis , mechanics , physics , magnetic field , thermodynamics , quantum mechanics , economics , economic growth
In this article, a streamline diffusion finite element method is proposed and analyzed for stationary incompressible magnetohydrodynamics (MHD) equations. This method is stable for any combinations of velocity, pressure, and magnet finite element spaces, without requiring Ladyzenskaja‐Babuška‐Brezzi (LBB) condition. The well‐posedness and convergence (at optimal error rate) of this scheme are proved in terms of some conditions. Two numerical experiments are illustrated to validate our theoretical analysis and show the streamline diffusion finite element approach is effective for solving the MHD problems. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1877–1901, 2014