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Convergent finite element discretizations of the nonstationary incompressible magnetohydrodynamics system. (English) Zbl 1149.76029
Summary: The incompressible MHD equations couple Navier-Stokes equations with Maxwell equations to describe the flow of a viscous incompressible electrically conducting fluid in a Lipschitz domain $\Omega \subset \Bbb {R} ^3$. We verify convergence of iterates of different coupling and decoupling fully discrete schemes towards weak solutions for vanishing discretization parameters. Optimal first-order of convergence is shown in the presence of strong solutions for a splitting scheme which decouples the computation of velocity field, pressure, and magnetic fields at every iteration step.

76M10Finite element methods (fluid mechanics)
76W05Magnetohydrodynamics and electrohydrodynamics
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
Full Text: DOI EuDML
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