Structure-preserving finite element methods for stationary MHD models

Kaibo Hu, Jinchao Xu

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We develop a class of mixed finite element schemes for stationary magnetohydrodynamics (MHD) models, using the magnetic field B and the current density j as discretization variables. We show that Gauss's law for the magnetic field, namely ∇· B = 0, and the energy law for the entire system are exactly preserved in the finite element schemes. Based on some new basic estimates for H(div) finite elements, we show that the new finite element scheme is well-posed. Furthermore, we show the existence of solutions to the nonlinear problems and the convergence of the Picard iterations and the finite element methods under some conditions.

Original languageEnglish (US)
Pages (from-to)553-581
Number of pages29
JournalMathematics of Computation
Volume88
Issue number316
DOIs
StatePublished - Jan 1 2019

Fingerprint

Magnetohydrodynamics
Finite Element Method
Magnetic fields
Finite Element
Finite element method
Magnetic Field
Picard Iteration
Current density
Mixed Finite Elements
Gauss
Nonlinear Problem
Existence of Solutions
Discretization
Entire
Model
Energy
Estimate

Keywords

  • Divergence-free
  • Finite element
  • MHD equations
  • Stationary

Cite this

Structure-preserving finite element methods for stationary MHD models. / Hu, Kaibo; Xu, Jinchao.

In: Mathematics of Computation, Vol. 88, No. 316, 01.01.2019, p. 553-581.

Research output: Contribution to journalArticle

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