Year: 2013
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 4 : pp. 904–919
Abstract
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'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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-IJNAM-603
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 4 : pp. 904–919
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Incompressible MHD equations Nonconforming mixed finite element method Optimal error estimates.