Volume 1, Issue 2
A High Physical Accuracy Method for Incompressible Magnetohydrodynamics

Michael A. Case ,  Alexander Labovsky and Leo G. Rebhol

Int. J. Numer. Anal. Mod. B, 1 (2010), pp. 217-236

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  • Abstract

We present an energy, cross-helicity and magnetic helicity preserving method for solving incompressible magnetohydrodynamic equations with strong enforcement of solenoidal constraints. The method is a semi-implicit Galerkin finite element discretization, that enforces pointwise solenoidal constraints by employing the Scott-Vogelius finite elements. We prove the unconditional stability of the method and the optimal convergence rate. We also perform several numerical tests verifying the effectiveness of our scheme and, in particular, its clear advantage over using the Taylor-Hood finite elements.

  • History

Published online: 2010-01

  • AMS Subject Headings

35R35, 49J40, 60G40

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