Convergent finite element discretization of the multi-fluid nonstationary incompressible magnetohydrodynamics equations

Banas L, Prohl A (2010)
Mathematics of Computation 79(272): 1957-1999.

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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.
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Banas L, Prohl A. Convergent finite element discretization of the multi-fluid nonstationary incompressible magnetohydrodynamics equations. Mathematics of Computation. 2010;79(272):1957-1999.
Banas, L., & Prohl, A. (2010). Convergent finite element discretization of the multi-fluid nonstationary incompressible magnetohydrodynamics equations. Mathematics of Computation, 79(272), 1957-1999. doi:10.1090/s0025-5718-10-02341-0
Banas, L., and Prohl, A. (2010). Convergent finite element discretization of the multi-fluid nonstationary incompressible magnetohydrodynamics equations. Mathematics of Computation 79, 1957-1999.
Banas, L., & Prohl, A., 2010. Convergent finite element discretization of the multi-fluid nonstationary incompressible magnetohydrodynamics equations. Mathematics of Computation, 79(272), p 1957-1999.
L. Banas and A. Prohl, “Convergent finite element discretization of the multi-fluid nonstationary incompressible magnetohydrodynamics equations”, Mathematics of Computation, vol. 79, 2010, pp. 1957-1999.
Banas, L., Prohl, A.: Convergent finite element discretization of the multi-fluid nonstationary incompressible magnetohydrodynamics equations. Mathematics of Computation. 79, 1957-1999 (2010).
Banas, Lubomir, and Prohl, Andreas. “Convergent finite element discretization of the multi-fluid nonstationary incompressible magnetohydrodynamics equations”. Mathematics of Computation 79.272 (2010): 1957-1999.
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