A Phase-Space Discontinuous Galerkin Scheme for the Radiative Transfer Equation in Slab Geometry

Matthias Schlottbom*, Olena Palii, Fleurianne Bertrand, Riccardo Bardin

*Corresponding author for this work

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Abstract

We derive and analyze a symmetric interior penalty discontinuous Galerkin scheme for the approximation of the second-order form of the radiative transfer equation in slab geometry. Using appropriate trace lemmas, the analysis can be carried out as for more standard elliptic problems. Supporting examples show the accuracy and stability of the method also numerically, for different polynomial degrees. For discretization, we employ quad-tree grids, which allow for local refinement in phase-space, and we show exemplary that adaptive methods can efficiently approximate discontinuous solutions. We investigate the behavior of hierarchical error estimators and error estimators based on local averaging.
Original languageEnglish
JournalComputational Methods in Applied Mathematics
Early online date21 Feb 2024
DOIs
Publication statusE-pub ahead of print/First online - 21 Feb 2024

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