A Low Order Nonconforming Mixed Finite Element Method for Non-Stationary Incompressible Magnetohydrodynamics System
Year: 2023
Author: Zhiyun Yu, Dongyang Shi, Huiqing Zhu
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 4 : pp. 569–587
Abstract
A low order nonconforming mixed finite element method (FEM) is established for the fully coupled non-stationary incompressible magnetohydrodynamics (MHD) problem in a bounded domain in 3D. The lowest order finite elements on tetrahedra or hexahedra are chosen to approximate the pressure, the velocity field and the magnetic field, in which the hydrodynamic unknowns are approximated by inf-sup stable finite element pairs and the magnetic field by $H^1(\Omega)$-conforming finite elements, respectively. The existence and uniqueness of the approximate solutions are shown. Optimal order error estimates of $L^2(H^1)$-norm for the velocity field, $L^2(L^2)$-norm for the pressure and the broken $L^2(H^1)$-norm for the magnetic field are derived.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2107-m2021-0114
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 4 : pp. 569–587
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Non-stationary incompressible MHD problem Nonconforming mixed FEM Optimal order error estimates.