A subgrid stabilization finite element method for incompressible magnetohydrodynamics

Date

2013-07-01

Author

Belenli, Mine A.
Kaya Merdan, Songül
Rebholz, Leo G.
Wilson, Nicholas E.

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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.

Subject Keywords

Finite element method, MHD, Subgrid stabilization, Stability analysis, Convergence analysis, Scott-Vogelius elements, 76W05, 65M60, 65M12

URI

https://hdl.handle.net/11511/32729

Journal

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

DOI

https://doi.org/10.1080/00207160.2012.758363

Collections

Department of Mathematics, Article

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Citation Formats

M. A. Belenli, S. Kaya Merdan, L. G. Rebholz, and N. E. Wilson, “A subgrid stabilization finite element method for incompressible magnetohydrodynamics,” INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, pp. 1506–1523, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32729.