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

Giani, S.

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: Jan 31, 2019
• 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