The multiscale enrichment finite volumemethod for the stationary incompressible magnetohydrodynamics flow

SHEN Xiao-Rong; ZHANG Tong; CHEN Chuan-Jun

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The multiscale enrichment finite volumemethod for the stationary incompressible magnetohydrodynamics flow

SHEN Xiao-Rong,ZHANG Tong *,CHEN Chuan-Jun

School of Mathematics and Information Sciences, Yantai University, Yantai, 264005

*Correspondence author

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Funding: ***Foundation （No.00000000）, *** Foundation （No.00000000）, ZR2021MA010)and NSF of Henan Province （No.No.202300410167）

Opened online:18 April 2023

Accepted by: none

Citation: SHEN Xiao-Rong,ZHANG Tong,CHEN Chuan-Jun.The multiscale enrichment finite volumemethod for the stationary incompressible magnetohydrodynamics flow[OL]. [18 April 2023] http://en.paper.edu.cn/en_releasepaper/content/4759648

In the paper, the finite volume method for the steady incompressible magnetohydrodynamics(MHD) problem based on the lowest order mixed finite element pair on triangular mesh is considered, the linear polynomial is used to approximate the velocity and magnetic fields and the piecewise constant is adopted to approximate the pressure. In order to overcome the restriction of discrete inf-sup (LBB) condition, the multiscale enrichment method is employed. Firstly, the existence, uniqueness and stability of numerical solutions are established through the fixed point theorem. Then, the optimal error estimates of numerical solutions in H1 and L2-norms are presented. Finally, some numerical results are provided to verify the established theoretical findings and show the performances of considered numerical scheme.

Keywords:Computational mathematics; finite volume method; multiscale enrichment method; magnetohydrodynamics ﬂow; stability; error estimates.

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