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On the Role of Involutions in the Discontinuous Galerkin Discretization of Maxwell and Magnetohydrodynamic Systems

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Compatible Spatial Discretizations

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 142))

Abstract

The role of involutions in energy stability of the discontinuous Galerkin (DG) discretization of Maxwell and magnetohydrodynamic (MHD) systems is examined. Important differences are identified in the symmetrization of the Maxwell and MHD systems that impact the construction of energy stable discretizations using the DG method. Specifically, general sufficient conditions to be imposed on the DG numerical flux and approximation space are given so that energy stability is retained. These sufficient conditions reveal the favorable energy consequence of imposing continuity in the normal component of the magnetic induction field at interelement boundaries for MHD discretizations. Counterintuitively, this condition is not required for stability of Maxwell discretizations using the discontinuous Galerkin method.

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Author information

Authors and Affiliations

  1. NASA Ames Research Center, M.S. T27A-1, Moffett Field, CA, 94035-1000, USA

    Timothy Barth

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  1. Timothy Barth
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Editor information

Editors and Affiliations

  1. Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN, 55455, USA

    Douglas N. Arnold

  2. Computational Mathematics and Algorithms Department, Sandia National Laboratories, Alburquerque, NM, 87185-1110, USA

    Pavel B. Bochev  & Richard B. Lehoucq  & 

  3. Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213-3890, USA

    Roy A. Nicolaides

  4. Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Mikhail Shashkov

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© 2006 Springer Science+Business Media, LLC

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Barth, T. (2006). On the Role of Involutions in the Discontinuous Galerkin Discretization of Maxwell and Magnetohydrodynamic Systems. In: Arnold, D.N., Bochev, P.B., Lehoucq, R.B., Nicolaides, R.A., Shashkov, M. (eds) Compatible Spatial Discretizations. The IMA Volumes in Mathematics and its Applications, vol 142. Springer, New York, NY. https://doi.org/10.1007/0-387-38034-5_4

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