TY - JOUR
T1 - A Low Order Nonconforming Mixed Finite Element Method for Non-Stationary Incompressible Magnetohydrodynamics System
AU - Yu , Zhiyun
AU - Shi , Dongyang
AU - Zhu , Huiqing
JO - Journal of Computational Mathematics
VL - 4
SP - 569
EP - 587
PY - 2023
DA - 2023/02
SN - 41
DO - http://doi.org/10.4208/jcm.2107-m2021-0114
UR - https://global-sci.org/intro/article_detail/jcm/21406.html
KW - Non-stationary incompressible MHD problem, Nonconforming mixed FEM, Optimal order error estimates.
AB - <p style="text-align: justify;">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.</p>