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A Mixed DG Method for Linearized Incompressible Magnetohydrodynamics

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Abstract

We introduce and analyze a discontinuous Galerkin method for the numerical discretization of a stationary incompressible magnetohydrodynamics model problem. The fluid unknowns are discretized with inf-sup stable discontinuous ℘ 3 k −℘ k−1 elements whereas the magnetic part of the equations is approximated by discontinuous ℘ 3 k −℘ k+1 elements. We carry out a complete a-priori error analysis of the method and prove that the energy norm error is convergent of order k in the mesh size. These results are verified in a series of numerical experiments.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    Paul Houston

  2. Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada

    Dominik Schötzau & Xiaoxi Wei

Authors
  1. Paul Houston
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  2. Dominik Schötzau
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  3. Xiaoxi Wei
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Corresponding author

Correspondence to Dominik Schötzau.

Additional information

D. Schötzau and X. Wei were supported in part by the Natural Sciences and Engineering Research Counsil of Canada (NSERC).

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Houston, P., Schötzau, D. & Wei, X. A Mixed DG Method for Linearized Incompressible Magnetohydrodynamics. J Sci Comput 40, 281–314 (2009). https://doi.org/10.1007/s10915-008-9265-x

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  • DOI: https://doi.org/10.1007/s10915-008-9265-x

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