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Decoupled schemes for unsteady MHD equations. I. time discretization
Author(s) -
Zhang GuoDong,
He Yinnian
Publication year - 2017
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.22132
Subject(s) - discretization , mathematics , convergence (economics) , magnetohydrodynamics , stability (learning theory) , finite element method , partial differential equation , scheme (mathematics) , mathematical analysis , computer science , physics , magnetic field , quantum mechanics , machine learning , economics , thermodynamics , economic growth
In this article, a time discretization decoupled scheme for two‐dimensional magnetohydrodynamics equations is proposed. The almost unconditional ( Δ t ≤ C )H 2stability and convergence of this scheme are provided. The optimalL 2 − H 1error estimates for velocity and magnet are provided, and the optimalL 2error estimate for pressure are deduced as well. Finite element spatial discretization and numerical implementation are considered in our article (Zhang and He, Comput Math Appl 69 (2015), 1390–1406). © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 956–973, 2017