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

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

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

Published online: 2010-01

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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.
  • Keywords

MHD Cross-helicity Magnetic-helicity Scott-Vogelius elements

  • AMS Subject Headings

35R35 49J40 60G40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAMB-1-217, author = {Michael A. Case, Alexander Labovsky, Leo G. Rebhol}, title = {A High Physical Accuracy Method for Incompressible Magnetohydrodynamics}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2010}, volume = {1}, number = {2}, pages = {217--236}, 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.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/333.html} }
TY - JOUR T1 - A High Physical Accuracy Method for Incompressible Magnetohydrodynamics AU - Michael A. Case, Alexander Labovsky, Leo G. Rebhol JO - International Journal of Numerical Analysis Modeling Series B VL - 2 SP - 217 EP - 236 PY - 2010 DA - 2010/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/333.html KW - MHD KW - Cross-helicity KW - Magnetic-helicity KW - Scott-Vogelius elements AB - 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.
Michael A. Case, Alexander Labovsky, Leo G. Rebhol. (2010). A High Physical Accuracy Method for Incompressible Magnetohydrodynamics. International Journal of Numerical Analysis Modeling Series B. 1 (2). 217-236. doi:
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