{"paper":{"title":"Anisotropic hp space-time adaptivity and goal-oriented error control for convection-dominated problems","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.NA","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Bernhard Endtmayer, Marius Paul Bruchh\\\"auser, Nils Margenberg","submitted_at":"2026-02-14T18:25:22Z","abstract_excerpt":"We present an anisotropic goal-oriented error estimator based on the Dual Weighted Residual (DWR) method for time-dependent convection-dominated problems. Using elementwise p-anisotropic finite element spaces, the estimator is elementwise separated with respect to the single directions in space and time. This naturally leads to adaptive, anisotropic hp-refinement (h-anisotropic refinement and elementwise anisotropic p-enrichment). We employ discontinuous elements in space and time, which are well suited for problems with high Peclet numbers. Efficiency and robustness of the underlying algorith"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.13843","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.13843/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}