Convergent finite element discretizations of the nonstationary incompressible magnetohydrodynamics system

Prohl, Andreas

ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 6, pp. 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 $\Omega \subset {ℝ}^3$. 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.

Classification : 65N30
Mots clés : magneto-hydrodynamics, discretization, FEM, fixed-point scheme, splitting-method

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