Layton, W. J.; Meir, A. J.; Schmidt, P. G. A two-level discretization method for the stationary MHD equations. (English) Zbl 0898.76059 ETNA, Electron. Trans. Numer. Anal. 6, 198-210 (1997). Summary: We analyze a two-level finite-element method for discretizing the equations of stationary, viscous, incompressible magnetohydrodynamics. We treat the equations under physically realistic (“nonideal”) boundary conditions that account for the electromagnetic interaction of the fluid with the surrounding media. The suggested algorithm involves solving a small, nonlinear problem on a coarse mesh and then one large, linear problem on a fine mesh. We prove well-posedness of the algorithm and optimal error estimates under a small-data assumption. Cited in 35 Documents MSC: 76M10 Finite element methods applied to problems in fluid mechanics 76W05 Magnetohydrodynamics and electrohydrodynamics 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs Keywords:Navier-Stokes equations; Maxwell’s equations; variational methods; coarse mesh; fine mesh; well-posedness; optimal error estimates PDFBibTeX XMLCite \textit{W. J. Layton} et al., ETNA, Electron. Trans. Numer. Anal. 6, 198--210 (1997; Zbl 0898.76059) Full Text: EuDML EMIS