Convergence of a B-E based finite element method for MHD models on Lipschitz domains

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Original languageEnglish
Article number112477
Journal / PublicationJournal of Computational and Applied Mathematics
Online published14 Oct 2019
Publication statusPublished - Apr 2020


We discuss a class of magnetic–electric fields based finite element schemes for stationary magnetohydrodynamics (MHD) systems with two types of boundary conditions. We establish a key L3 estimate for divergence-free finite element functions for a new type of boundary conditions. With this estimate and a similar one in Hu and Xu (2018), we rigorously prove the convergence of Picard iterations and the finite element schemes with weak regularity assumptions. These results demonstrate the convergence of the finite element methods for singular solutions.

Research Area(s)

  • de Rham complex, Finite element method, Magnetohydrodynamics, Structure-preserving