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Reliable anisotropic-adaptive discontinuous Galerkin method for simplified P_N approximations of radiative transfer

Giani, S.

Reliable anisotropic-adaptive discontinuous Galerkin method for simplified P_N approximations of radiative transfer Thumbnail


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Abstract

In this paper we present the analysis for the error estimator for radiative transfer problems presented in Giani and Seaid (2016) where we showed the capabilities of the error estimator to accurately drive the adaptivity to resolve steep boundary layers, which are among the difficulties that most numerical methods fail to resolve accurately. We prove reliability for the error estimator in terms of a global upper bound of the error measured in the natural norm. We present a series of numerical experiments to test the efficiency of this approach within a fully automated hp-adaptive refinement algorithm.

Citation

Giani, S. (2018). Reliable anisotropic-adaptive discontinuous Galerkin method for simplified P_N approximations of radiative transfer. Journal of Computational and Applied Mathematics, 337, 225-243. https://doi.org/10.1016/j.cam.2017.12.039

Journal Article Type Article
Acceptance Date Jan 4, 2018
Online Publication Date Jan 31, 2018
Publication Date Aug 1, 2018
Deposit Date Jan 4, 2018
Publicly Available Date Mar 29, 2024
Journal Journal of Computational and Applied Mathematics
Print ISSN 0377-0427
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 337
Pages 225-243
DOI https://doi.org/10.1016/j.cam.2017.12.039

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