TY - JOUR
T1 - Nonconforming Mixed Finite Element Methods for Stationary Incompressible Magnetohydrodynamics
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 904
EP - 919
PY - 2013
DA - 2013/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/603.html
KW - Incompressible MHD equations, Nonconforming mixed finite element method, Optimal error estimates.
AB - <p style="text-align: justify;">The main aim of this paper is to study the approximation of nonconforming mixed finite element methods for stationary, incompressible magnetohydrodynamics (MHD) equations
in 3D. A family of nonconforming finite elements are taken as the approximation spaces for the
velocity field, the piecewise constant element for the pressure and the Nédélec&#39;s element with the
lowest order for the magnetic field on hexahedra or tetrahedra. A new simple method is adopted to
prove the discrete Poincaré-Friedrichs inequality instead of the discrete Helmholtz decomposition
method. The existence and uniqueness of the approximate solutions are shown. The convergence
analysis is presented and the optimal order error estimates for the pressure in $L^2$-norm, as well
as those in a broken $H^1$-norm for the velocity field and H($curl$)-norm for the magnetic field are
derived.</p>