A least squares finite element method using Elsasser variables for magnetohydrodynamic equations

Eunjung Lee, Heonkyu Ha, Sang Dong Kim

Research output: Contribution to journalArticle

Abstract

There are various different forms of magnetohydrodynamic(MHD) equations and they have been studied for years due to its complicated coupling between variables. This paper proposes to use an equivalently transformed MHD equations with Elsasser variables and the least squares finite element method to find the approximation to them. Introducing new variables by combining fluid velocity and magnetic field yields a Navier–Stokes like system. Then the first-order system least squares method using displacement recasts the transformed MHD equations into a system of first order partial differential equations and the Newton's algorithm linearizes the problem. An L2-residual functional is defined to minimize and the unique existence of corresponding weak solution is shown. Finally, the convergence of proposed approximation is analyzed and several numerical examples are presented to verify the theory.

LanguageEnglish
Pages599-608
Number of pages10
JournalJournal of Computational and Applied Mathematics
Volume346
DOIs
Publication statusPublished - 2019 Jan 15

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Least-squares Finite Element Method
Magnetohydrodynamic Equations
Magnetohydrodynamics
Finite element method
First-order System
First order differential equation
Approximation
Navier-Stokes
Least Square Method
Velocity Field
Partial differential equations
Weak Solution
Partial differential equation
Magnetic Field
Magnetic fields
Verify
Minimise
Fluid
Numerical Examples
Fluids

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

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A least squares finite element method using Elsasser variables for magnetohydrodynamic equations. / Lee, Eunjung; Ha, Heonkyu; Kim, Sang Dong.

In: Journal of Computational and Applied Mathematics, Vol. 346, 15.01.2019, p. 599-608.

Research output: Contribution to journalArticle

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