{"id":"https://openalex.org/W7224853663","doi":"https://doi.org/10.48550/arxiv.2610.39299","title":"Energy Stability and Error Estimates for a Globally Divergence-Free DG Method of Arbitrary Order","display_name":"Energy Stability and Error Estimates for a Globally Divergence-Free DG Method of Arbitrary Order","publication_year":2026,"publication_date":"2026-10-29","ids":{"openalex":"https://openalex.org/W7224853663","doi":"https://doi.org/10.48550/arxiv.2610.39299"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.39299","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39299","pdf_url":"https://arxiv.org/pdf/2610.39299","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/2610.39299","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5115596944","display_name":"Yuchang Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu, Yuchang","raw_affiliation_strings":["School of Mathematical Sciences , University of Science and Technology of China , Hefei , Anhui 230026 , P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , University of Science and Technology of China , Hefei , Anhui 230026 , P.R. China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5160220731","display_name":"Yan Jiang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiang, Yan","raw_affiliation_strings":["School of Mathematical Sciences , University of Science and Technology of China , Hefei , Anhui 230026 , P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , University of Science and Technology of China , Hefei , Anhui 230026 , P.R. China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5123979588","display_name":"Mengping Zhang","orcid":"https://orcid.org/0009-0000-6502-073X","observed_orcids":["https://orcid.org/0009-0000-6502-073X"]},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Mengping","raw_affiliation_strings":["School of Mathematical Sciences , University of Science and Technology of China , Hefei , Anhui 230026 , P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , University of Science and Technology of China , Hefei , Anhui 230026 , P.R. China","institution_ids":["https://openalex.org/I126520041"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I126520041"],"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":0.9961000084877014,"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":0.9961000084877014,"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":0.0026000000070780516,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/energy-stability","display_name":"energy stability","score":0.8370000123977661},{"id":"https://openalex.org/keywords/a-priori-error-estimates","display_name":"a priori error estimates","score":0.9639999866485596},{"id":"https://openalex.org/keywords/higher-order-finite-elements","display_name":"high-order finite elements","score":0.625},{"id":"https://openalex.org/keywords/unstructured-triangular-meshes","display_name":"unstructured triangular meshes","score":0.8399999737739563}],"concepts":[{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.7978000044822693},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7197999954223633},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5864999890327454},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5522000193595886},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5338000059127808},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5126000046730042},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.5002999901771545},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4950999915599823},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4765999913215637},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.47130000591278076},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43790000677108765},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4336000084877014},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.4250999987125397},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4180000126361847},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3797999918460846},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.37290000915527344},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.3400000035762787},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.31859999895095825},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.31690001487731934},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.313400000333786},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.3091000020503998},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.30799999833106995},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30239999294281006},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.30090001225471497},{"id":"https://openalex.org/C131357438","wikidata":"https://www.wikidata.org/wiki/Q208598","display_name":"Eddy current","level":2,"score":0.2865999937057495},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2793999910354614},{"id":"https://openalex.org/C2780033567","wikidata":"https://www.wikidata.org/wiki/Q6823720","display_name":"Method of moments (probability theory)","level":3,"score":0.27129998803138733},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.2712000012397766},{"id":"https://openalex.org/C19579662","wikidata":"https://www.wikidata.org/wiki/Q461145","display_name":"Energy operator","level":3,"score":0.25949999690055847},{"id":"https://openalex.org/C2989268449","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Energy method","level":2,"score":0.25380000472068787},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.39299","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39299","pdf_url":"https://arxiv.org/pdf/2610.39299","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.2610.39299","doi":"https://doi.org/10.48550/arxiv.2610.39299","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.39299","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.39299","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39299","pdf_url":"https://arxiv.org/pdf/2610.39299","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/W7224853663.pdf","grobid_xml":"https://content.openalex.org/works/W7224853663.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4416344982","https://openalex.org/W4416263138","https://openalex.org/W2116093909","https://openalex.org/W2743672113","https://openalex.org/W7215080956","https://openalex.org/W7095607958","https://openalex.org/W2011571988","https://openalex.org/W3032084932","https://openalex.org/W1549892706","https://openalex.org/W4408866278"],"abstract_inverted_index":{"We":[0],"propose":[1],"and":[2,87,113],"analyze":[3],"an":[4],"arbitrary-order":[5],"globally":[6],"divergence-free":[7],"(GDF)":[8],"discontinuous":[9],"Galerkin":[10],"(DG)":[11],"method":[12],"for":[13,119],"the":[14,25,32,48,61,73,93,125],"two-dimensional":[15],"linear":[16],"magnetic":[17,63],"induction":[18],"equation":[19],"on":[20,60],"unstructured":[21],"triangular":[22],"meshes.":[23],"To":[24],"best":[26],"of":[27,41],"our":[28],"knowledge,":[29],"this":[30],"is":[31],"first":[33],"work":[34],"to":[35,72],"provide":[36],"a":[37,53,77,88,108,115],"rigorous":[38],"energy-based":[39],"analysis":[40],"high-order":[42,95],"GDF-DG":[43],"methods.":[44],"First,":[45],"we":[46,67,102],"incorporate":[47],"edge":[49],"normal-trace":[50],"evolution":[51],"into":[52],"closed,":[54],"strictly":[55],"local":[56,70,84],"semidiscrete":[57,104],"operator":[58],"acting":[59],"elementwise":[62],"field":[64],"alone.":[65],"Then,":[66],"introduce":[68],"two":[69],"modifications":[71],"continuous":[74],"electric":[75],"field:":[76],"weighted":[78],"patch":[79],"moment":[80],"correction":[81],"that":[82,91],"enforces":[83],"polynomial":[85],"orthogonality":[86],"vertex-patch":[89],"stabilization":[90],"damps":[92],"remaining":[94],"modes.":[96],"On":[97],"shape-regular,":[98],"quasi-uniform":[99],"periodic":[100],"triangulations,":[101],"prove":[103],"energy":[105],"stability":[106],"with":[107],"sufficiently":[109],"large":[110],"mesh-independent":[111],"penalty":[112],"establish":[114],"priori":[116],"error":[117],"estimates":[118],"smooth":[120],"solutions.":[121],"Numerical":[122],"experiments":[123],"support":[124],"analysis.":[126]},"counts_by_year":[],"updated_date":"2026-11-02T09:45:03.842371","created_date":"2026-10-31T00:00:00"}
