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, vol.90, no.7, pp.1506-1523, 2013 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 90 Issue: 7
  • Publication Date: 2013
  • Doi Number: 10.1080/00207160.2012.758363
  • Journal Name: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.1506-1523
  • Keywords: finite element method, MHD, subgrid stabilization, stability analysis, convergence analysis, Scott-Vogelius elements, 76W05, 65M60, 65M12, MODIFIED NAVIER-STOKES, PARA-VERSION, DISCRETIZATION, APPROXIMATIONS, FLOWS

Abstract

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.