A subgrid stabilization finite element method for incompressible magnetohydrodynamics


Belenli M. A. , KAYA MERDAN S. , Rebholz L. G. , Wilson N. E.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, cilt.90, ss.1506-1523, 2013 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 90 Konu: 7
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1080/00207160.2012.758363
  • Dergi Adı: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
  • Sayfa Sayıları: ss.1506-1523

Özet

This paper studies a numerical scheme for approximating solutions of incompressible magnetohydrodynamic (MHD) equations that uses eddy viscosity stabilization only on the small scales of the fluid flow. This stabilization scheme for MHD equations uses a Galerkin finite element spatial discretization with Scott-Vogelius mixed finite elements and semi-implicit backward Euler temporal discretization. We prove its unconditional stability and prove how the coarse mesh can be chosen so that optimal convergence can be achieved. We also provide numerical experiments to confirm the theory and demonstrate the effectiveness of the scheme on a test problem for MHD channel flow.