{"paper":{"title":"Naturally curved quadrilateral mesh generation using an adaptive spectral element solver","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.NA"],"primary_cat":"math.NA","authors_text":"David A. Kopriva, Joaquim Peir\\'o, Julian Marcon, Spencer J. Sherwin","submitted_at":"2019-08-12T17:35:01Z","abstract_excerpt":"We describe an adaptive version of a method for generating valid naturally curved quadrilateral meshes. The method uses a guiding field, derived from the concept of a cross field, to create block decompositions of multiply connected two dimensional domains. The a priori curved quadrilateral blocks can be further split into a finer high-order mesh as needed. The guiding field is computed by a Laplace equation solver using a continuous Galerkin or discontinuous Galerkin spectral element formulation. This operation is aided by using $p$-adaptation to achieve faster convergence of the solution wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04272","kind":"arxiv","version":2},"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/1908.04272/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"}