Analysis of a semi-implicit structure-preserving finite element method for the nonstationary incompressible Magnetohydrodynamics equations

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Original languageEnglish
Pages (from-to)2150-2161
Journal / PublicationComputers and Mathematics with Applications
Issue number10
Online published25 Sep 2020
Publication statusPublished - 15 Nov 2020


We revise the structure-preserving finite element method in [K. Hu, Y. MA and J. Xu. (2017) Stable finite element methods preserving ∇⋅B=0 exactly for MHD models. Numer. Math., 135, 371-396]. The revised method is semi-implicit in time-discretization. We prove the linearized scheme preserves the divergence free property for the magnetic field exactly at each time step. Further, we showed the linearized scheme is unconditionally stable and we obtain optimal convergence in the energy norm of the revised method even for solutions with low regularity.

Research Area(s)

  • Finite element method, Magnetohydrodynamics, Structure-preserving

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