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Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations pp 181–193Cite as

Discontinuous Galerkin for the Radiative Transport Equation

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Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 157))

Abstract

This note presents some recent results regarding the approximation of the linear radiative transfer equation using discontinuous Galerkin methods. The locking effect occurring in the diffusion limit with the upwind numerical flux is investigated and a correction technique is proposed.

AMS(MOS) subject classifications. 65N35, 65N22, 65F05, 35J05

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Notes

  1. 1.

    The term “flux” is used in two different contexts. In the radiation transport context, we use the terms “angular flux” and “scalar flux.” In the DG context, we use the notion of “numerical flux.” These two notions are unfortunately unrelated but commonly employed in the radiation transport and DG literature, respectively. To avoid confusion, we always try to use the proper adjective in this paper.

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Acknowledgements

This material is based upon work supported by the Department of Homeland Security under agreement 2008-DN-077-ARI018-02, National Science Foundation grants DMS-0713829, DMS-0810387, and CBET-0736202, and is partially supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).

Author information

Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, College Station, TX, 77843, USA

    Jean-Luc Guermond

  2. Heidelberg University, Im Neuenheimer Feld 368, 69120, Heidelberg, USA

    Guido Kanschat

  3. Department of Nuclear Engineering, Texas A&M University, College Station, TX, 77843, USA

    Jean C. Ragusa

Authors
  1. Jean-Luc Guermond
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  2. Guido Kanschat
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  3. Jean C. Ragusa
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Corresponding author

Correspondence to Jean-Luc Guermond .

Editor information

Editors and Affiliations

  1. Department of Mathematics, The University of Tennessee, Knoxville, Tennessee, USA

    Xiaobing Feng

  2. Department of Mathematics, The University of Tennessee, Knoxville, Tennessee, USA

    Ohannes Karakashian

  3. Department of Mathematics, The University of Tennessee, Knoxville, Tennessee, USA

    Yulong Xing

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Guermond, JL., Kanschat, G., Ragusa, J.C. (2014). Discontinuous Galerkin for the Radiative Transport Equation. In: Feng, X., Karakashian, O., Xing, Y. (eds) Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations. The IMA Volumes in Mathematics and its Applications, vol 157. Springer, Cham. https://doi.org/10.1007/978-3-319-01818-8_7

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