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Journal of Scientific Computing

Erschienen in:

29.11.2018

Optimal Error Estimates of Penalty Based Iterative Methods for Steady Incompressible Magnetohydrodynamics Equations with Different Viscosities

verfasst von: Haiyan Su, Shipeng Mao, Xinlong Feng

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2019

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Abstract

In this paper, we consider the penalty based finite element methods for the 2D/3D stationary incompressible magnetohydrodynamics (MHD) equations with different Reynolds numbers. Penalty method is applied to address the incompressible constraint “\(div \,\mathbf{u }=0\)” based on two different finite element pairs \(P_{1}{-}P_{0}{-}P_{1}\) and \(P_{1}b{-}P_{1}{-}P_{1}b\). Furthermore, the proposed methods are the interesting combination of three different iterations and two-level finite element algorithm such that the uniqueness condition holds. Besides, the rigorous analysis of stability and optimal error estimate with respect to the penalty parameter \(\epsilon \) for the proposed methods are given. Extensive 2D/3D numerical tests demonstrated the competitive performance of penalty methods.

Vorheriger Artikel Image Segmentation Using the Cahn–Hilliard Equation

Nächster Artikel A High Order Semi-Lagrangian Discontinuous Galerkin Method for the Two-Dimensional Incompressible Euler Equations and the Guiding Center Vlasov Model Without Operator Splitting

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Titel: Optimal Error Estimates of Penalty Based Iterative Methods for Steady Incompressible Magnetohydrodynamics Equations with Different Viscosities
verfasst von: Haiyan Su
Shipeng Mao
Xinlong Feng
Publikationsdatum: 29.11.2018
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2/2019
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-018-0883-7

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