A convergent linearized lagrange finite element method for the magneto-hydrodynamic equations in two-dimensional nonsmooth and nonconvex domains

Buyang Li, Jilu Wang, Liwei Xu (Corresponding Author)

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)

Abstract

A new fully discrete linearized H1-conforming Lagrange finite element method is proposed for solving the two-dimensional magneto-hydrodynamics equations based on a magnetic potential formulation. The proposed method yields numerical solutions that converge in general domains that may be nonconvex, nonsmooth, and multiconnected. The convergence of subsequences of the numerical solutions is proved only based on the regularity of the initial conditions and source terms without extra assumptions on the regularity of the solution. Strong convergence in L2(0, T;L2(Ω)) was proved for the numerical solutions of both u and H without any mesh restriction.

Original languageEnglish
Pages (from-to)430-459
Number of pages30
JournalSIAM Journal on Numerical Analysis
Volume58
Issue number1
DOIs
Publication statusPublished - 23 Jan 2020

Keywords

  • Convergence
  • Finite element
  • H1-conforming
  • MHD
  • Nonconvex
  • Nonsmooth

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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