Convergent finite element discretizations of the nonstationary incompressible magnetohydrodynamics system
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 6, p. 1065-1087

The incompressible MHD equations couple Navier-Stokes equations with Maxwell’s equations to describe the flow of a viscous, incompressible, and electrically conducting fluid in a Lipschitz domain Ω 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.

DOI : https://doi.org/10.1051/m2an:2008034
Classification:  65N30
Keywords: magneto-hydrodynamics, discretization, FEM, fixed-point scheme, splitting-method
@article{M2AN_2008__42_6_1065_0,
     author = {Prohl, Andreas},
     title = {Convergent finite element discretizations of the nonstationary incompressible magnetohydrodynamics system},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {6},
     year = {2008},
     pages = {1065-1087},
     doi = {10.1051/m2an:2008034},
     zbl = {1149.76029},
     mrnumber = {2473320},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2008__42_6_1065_0}
}
Prohl, Andreas. Convergent finite element discretizations of the nonstationary incompressible magnetohydrodynamics system. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 6, pp. 1065-1087. doi : 10.1051/m2an:2008034. http://www.numdam.org/item/M2AN_2008__42_6_1065_0/

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