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Magnetic-Electric Formulations for Stationary Magnetohydrodynamics Models. (arXiv:1711.11330v1 [math.NA])

来源于:arXiv
We discuss magnetic-electric fields based finite element schemes for stationary magnetohydrodynamics (MHD) systems with two types of boundary conditions. The schemes are unconditional well-posed and stable. Moreover, magnetic Gauss's law $\nabla\cdot\bm{B}=0$ is preserved precisely on the discrete level. We establish a key $L^{3}$ estimate for divergence-free finite element functions for a new type of boundary condition. With this estimate and a similar one in \cite{hu2015structure}, we rigorously prove the convergence of Picard iterations and the finite element schemes. These results show that the proposed finite element methods converge for singular solutions. 查看全文>>