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

Giani, S. (2018) 'Reliable anisotropic-adaptive discontinuous Galerkin method for simplified P_N approximations of radiative transfer.', Journal of computational and applied mathematics., 337 . pp. 225-243.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.cam.2017.12.039
Publisher statement:© 2018 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Date accepted:04 January 2018
Date deposited:04 January 2018
Date of first online publication:31 January 2018
Date first made open access:31 January 2019

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