{"paper":{"title":"Hidden Accuracy and Superconvergence Analysis of Central Discontinuous Galerkin Methods on Overlapping Meshes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Kailiang Wu, Manting Peng","submitted_at":"2026-06-30T16:37:50Z","abstract_excerpt":"This paper establishes the first rigorous superconvergence theory for semidiscrete and fully discrete central discontinuous Galerkin (CDG) methods for linear hyperbolic equations on overlapping meshes. While the optimal $L^2$ convergence of $\\mathbb{Q}^k$ CDG schemes was established on uniform Cartesian meshes by Liu, Shu, and Zhang [ SIAM J. Numer. Anal.}, 56 (2018), pp. 520--541], their observed $\\mathcal{O}(h^{k+2})$ pointwise superconvergence has remained unproven, due to the loss of standard single-mesh Galerkin orthogonality inherent in the CDG overlapping structure.\n  To overcome this f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31931","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/2606.31931/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"}