### 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 L^{2}-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.

Original language | English |
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Pages (from-to) | 599-608 |

Number of pages | 10 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 346 |

DOIs | |

Publication status | Published - 2019 Jan 15 |

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### All Science Journal Classification (ASJC) codes

- Computational Mathematics
- Applied Mathematics

### Cite this

*Journal of Computational and Applied Mathematics*,

*346*, 599-608. https://doi.org/10.1016/j.cam.2018.06.038

}

*Journal of Computational and Applied Mathematics*, vol. 346, pp. 599-608. https://doi.org/10.1016/j.cam.2018.06.038

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - A least squares finite element method using Elsasser variables for magnetohydrodynamic equations

AU - Lee, Eunjung

AU - Ha, Heonkyu

AU - Kim, Sang Dong

PY - 2019/1/15

Y1 - 2019/1/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85051370302&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85051370302&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2018.06.038

DO - 10.1016/j.cam.2018.06.038

M3 - Article

VL - 346

SP - 599

EP - 608

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

ER -