AIMS Mathematics, 2020, 5(4): 3922-3951. doi: 10.3934/math.2020254.

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A modified characteristics projection finite element method for unsteady incompressible Magnetohydrodynamics equations

School of Mathematics and Information Science, Henan Polytechnic University, 454003, Jiaozuo, P. R. China

This paper provides a modified characteristics projection finite element method for the unsteady incompressible magnetohydrodynamics(MHD) equations. In this method, modified characteristics finite element method and the projection method will be combined for solving the unsteady incompressible MHD equations. Both the stability and the optimal error estimates both in L2 and H1 norms for the modified characteristics projection finite element method will be shown. In order to demonstrate the effectiveness of our method, we will present some numerical results at the end.
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Keywords unsteady incompressible MHD equations; finite element method; projection method; error estimates; modified characteristics projection method

Citation: Shujie Jing, Jixiang Guan, Zhiyong Si. A modified characteristics projection finite element method for unsteady incompressible Magnetohydrodynamics equations. AIMS Mathematics, 2020, 5(4): 3922-3951. doi: 10.3934/math.2020254

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