TY - JOUR
T1 - Convergent finite element discretization of the multi-fluid nonstationary incompressible magnetohydrodynamics equations
AU - Banas, Lubomir
AU - Prohl, Andreas
PY - 2010/10
Y1 - 2010/10
N2 - We propose a convergent implicit stabilized finite element discretization of the nonstationary incompressible magnetohydrodynamics equations with variable density, viscosity, and electric conductivity. The discretization satisfies a discrete energy law, and a discrete maximum principle for the positive density, and iterates converge to weak solutions of the limiting problem for vanishing discretization parameters. A simple fixed point scheme, together with an appropriate stopping criterion is proposed, which decouples the computation of density, velocity, and magnetic field, and inherits the above properties, provided a mild mesh constraint holds. Computational studies are provided. © 2010 American Mathematical Society.
AB - We propose a convergent implicit stabilized finite element discretization of the nonstationary incompressible magnetohydrodynamics equations with variable density, viscosity, and electric conductivity. The discretization satisfies a discrete energy law, and a discrete maximum principle for the positive density, and iterates converge to weak solutions of the limiting problem for vanishing discretization parameters. A simple fixed point scheme, together with an appropriate stopping criterion is proposed, which decouples the computation of density, velocity, and magnetic field, and inherits the above properties, provided a mild mesh constraint holds. Computational studies are provided. © 2010 American Mathematical Society.
UR - http://www.scopus.com/inward/record.url?scp=77956592131&partnerID=8YFLogxK
U2 - 10.1090/S0025-5718-10-02341-0
DO - 10.1090/S0025-5718-10-02341-0
M3 - Article
SN - 0025-5718
VL - 79
SP - 1957
EP - 1999
JO - Mathematics of Computation
JF - Mathematics of Computation
IS - 272
ER -