{"id":"https://openalex.org/W7213616998","doi":"https://doi.org/10.48550/arxiv.2609.23326","title":"Super-approximation and optimal $L^2$ convergence of the stabilized BGN method with piecewise linear parametric finite elements for curve-shortening flow","display_name":"Super-approximation and optimal $L^2$ convergence of the stabilized BGN method with piecewise linear parametric finite elements for curve-shortening flow","publication_year":2026,"publication_date":"2026-09-20","ids":{"openalex":"https://openalex.org/W7213616998","doi":"https://doi.org/10.48550/arxiv.2609.23326"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.23326","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23326","pdf_url":"https://arxiv.org/pdf/2609.23326","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.23326","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023630746","display_name":"Genming Bai","orcid":"https://orcid.org/0000-0002-4138-8051","observed_orcids":["https://orcid.org/0000-0002-4138-8051"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bai, Genming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5023630746"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/curve-shortening-flow","display_name":"curve shortening flow","score":0.9710000157356262},{"id":"https://openalex.org/keywords/superconvergence","display_name":"superconvergence","score":0.8519999980926514},{"id":"https://openalex.org/keywords/summation-by-parts","display_name":"summation by parts","score":0.8489999771118164},{"id":"https://openalex.org/keywords/projection-error","display_name":"projection error","score":0.7900000214576721},{"id":"https://openalex.org/keywords/trajectory-error","display_name":"trajectory error","score":0.9079999923706055}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5899999737739563},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5741999745368958},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5670999884605408},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5655999779701233},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5382000207901001},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4871000051498413},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.48669999837875366},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.4661000072956085},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.42739999294281006},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2897999882698059},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2572999894618988}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:2609.23326","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23326","pdf_url":"https://arxiv.org/pdf/2609.23326","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.23326","doi":"https://doi.org/10.48550/arxiv.2609.23326","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.23326","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.22850714","doi":"https://doi.org/10.5281/zenodo.22850714","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22850714","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.22850715","doi":"https://doi.org/10.5281/zenodo.22850715","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22850715","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.23326","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23326","pdf_url":"https://arxiv.org/pdf/2609.23326","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213616998.pdf","grobid_xml":"https://content.openalex.org/works/W7213616998.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7083305273","https://openalex.org/W7171884714"],"related_works":["https://openalex.org/W4403085932","https://openalex.org/W7213923252","https://openalex.org/W7171884714","https://openalex.org/W7214092334","https://openalex.org/W7220892975","https://openalex.org/W7204902132","https://openalex.org/W6960069858","https://openalex.org/W3048376425","https://openalex.org/W4416044930","https://openalex.org/W7118045801"],"abstract_inverted_index":{"We":[0],"develop":[1],"a":[2,21,66],"bihomotopy":[3],"argument":[4,19],"to":[5],"estimate":[6,24],"the":[7,26,32,38,41,53,62],"discrete":[8,44],"material":[9],"time":[10],"derivatives":[11],"of":[12,40,52,61,65],"consistency":[13,27],"functionals.":[14],"Combined":[15],"with":[16,31,37,73],"summation-by-parts,":[17],"this":[18],"yields":[20],"directional":[22],"super-convergence":[23,51],"for":[25,70],"contribution":[28],"when":[29],"tested":[30],"normal":[33],"error":[34,55,64],"velocity.":[35],"Together":[36],"super-approximation":[39],"reversely":[42],"weighted":[43],"normal,":[45],"these":[46],"techniques":[47],"establish":[48],"$L_t^\\infty":[49,58],"H_x^1$":[50],"projection":[54],"and":[56],"optimal":[57],"L_x^2$":[59],"convergence":[60],"trajectory":[63],"stabilized":[67],"BGN":[68],"method":[69],"curve-shortening":[71],"flow":[72],"piecewise":[74],"linear":[75],"parametric":[76],"finite":[77],"elements.":[78]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-20T00:00:00"}