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Using appropriate trace lemmas, the analysis can be carried out as for more standard elliptic problems.\nSupporting examples show the accuracy and stability of the method also numerically, for different polynomial degrees.\nFor 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.<\/jats:p>","DOI":"10.1515\/cmam-2023-0090","type":"journal-article","created":{"date-parts":[[2024,2,20]],"date-time":"2024-02-20T15:42:02Z","timestamp":1708443722000},"page":"557-576","source":"Crossref","is-referenced-by-count":3,"title":["A Phase-Space Discontinuous Galerkin Scheme for the Radiative Transfer Equation in Slab Geometry"],"prefix":"10.1515","volume":"24","author":[{"given":"Riccardo","family":"Bardin","sequence":"first","affiliation":[{"name":"Faculty of Electrical Engineering, Mathematics and Computer Science , [ 168081]University of Twente, Enschede , The Netherlands"}]},{"given":"Fleurianne","family":"Bertrand","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering, Mathematics and Computer Science , [ 168081]University of Twente, Enschede , The Netherlands"}]},{"given":"Olena","family":"Palii","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering, Mathematics and Computer Science , [ 168081]University of Twente, Enschede , The Netherlands"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2527-6498","authenticated-orcid":false,"given":"Matthias","family":"Schlottbom","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering, Mathematics and Computer Science , [ 168081]University of Twente, Enschede , The Netherlands"}]}],"member":"374","published-online":{"date-parts":[[2024,2,21]]},"reference":[{"key":"2024070116104877685_j_cmam-2023-0090_ref_001","doi-asserted-by":"crossref","unstructured":"M. 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