{"id":"https://openalex.org/W3210852515","doi":"https://doi.org/10.1090/mcom/3780","title":"Convergence to weak solutions of a space-time hybridized discontinuous Galerkin method for the incompressible Navier\u2013Stokes equations","display_name":"Convergence to weak solutions of a space-time hybridized discontinuous Galerkin method for the incompressible Navier\u2013Stokes equations","publication_year":2022,"publication_date":"2022-08-03","ids":{"openalex":"https://openalex.org/W3210852515","doi":"https://doi.org/10.1090/mcom/3780","mag":"3210852515"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3780","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3780","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2110.11920","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048905697","display_name":"Keegan L. A. Kirk","orcid":"https://orcid.org/0000-0003-1190-6708"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Keegan Kirk","raw_affiliation_strings":["Department of Applied Mathematics, University of Waterloo, Waterloo N2L 3G1, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Waterloo, Waterloo N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036514025","display_name":"Ay\u00e7\u0131l \u00c7e\u015fmeli\u0307o\u011flu","orcid":"https://orcid.org/0000-0001-8057-6349"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ay\u00e7\u0131l \u00c7e\u015fmeli\u0307o\u011flu","raw_affiliation_strings":["Department of Mathematics and Statistics, Oakland University, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Oakland University, U.S.A","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034917067","display_name":"Sander Rhebergen","orcid":"https://orcid.org/0000-0001-6036-0356"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Sander Rhebergen","raw_affiliation_strings":["Department of Applied Mathematics, University of Waterloo, Waterloo N2L 3G1, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Waterloo, Waterloo N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5048905697"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":0.3006,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.55836654,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"92","issue":"339","first_page":"147","last_page":"174"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/mathematics","display_name":"Mathematics","score":0.8910495042800903},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6657941341400146},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6102221012115479},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.6021065711975098},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5727822780609131},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.5540074706077576},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.55094975233078},{"id":"https://openalex.org/keywords/weak-convergence","display_name":"Weak convergence","score":0.4603097438812256},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.4552426040172577},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44267791509628296},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4296247363090515},{"id":"https://openalex.org/keywords/weak-solution","display_name":"Weak solution","score":0.42371276021003723},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.26450711488723755},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06577056646347046}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8910495042800903},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6657941341400146},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6102221012115479},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.6021065711975098},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5727822780609131},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.5540074706077576},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.55094975233078},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.4603097438812256},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.4552426040172577},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44267791509628296},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4296247363090515},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.42371276021003723},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.26450711488723755},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06577056646347046},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C76178495","wikidata":"https://www.wikidata.org/wiki/Q4808784","display_name":"Asset (computer security)","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/mcom/3780","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3780","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2110.11920","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2110.11920","pdf_url":"https://arxiv.org/pdf/2110.11920","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2110.11920","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2110.11920","pdf_url":"https://arxiv.org/pdf/2110.11920","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[],"awards":[{"id":"https://openalex.org/G3249392190","display_name":null,"funder_award_id":"RGPIN-05606-2015","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G423229456","display_name":null,"funder_award_id":"CGSD3-534997-2019","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":66,"referenced_works":["https://openalex.org/W560409768","https://openalex.org/W592911714","https://openalex.org/W616225202","https://openalex.org/W628726389","https://openalex.org/W1009522003","https://openalex.org/W1472249170","https://openalex.org/W1525219438","https://openalex.org/W1545761024","https://openalex.org/W1668437634","https://openalex.org/W1935825599","https://openalex.org/W1989813548","https://openalex.org/W2005632248","https://openalex.org/W2013813162","https://openalex.org/W2014339952","https://openalex.org/W2016012726","https://openalex.org/W2020236463","https://openalex.org/W2021303967","https://openalex.org/W2024343740","https://openalex.org/W2024488576","https://openalex.org/W2037701755","https://openalex.org/W2041441722","https://openalex.org/W2051751432","https://openalex.org/W2057101802","https://openalex.org/W2062861068","https://openalex.org/W2073078790","https://openalex.org/W2081513515","https://openalex.org/W2082621526","https://openalex.org/W2108495158","https://openalex.org/W2118395915","https://openalex.org/W2130214873","https://openalex.org/W2155061016","https://openalex.org/W2160623568","https://openalex.org/W2166587858","https://openalex.org/W2206365535","https://openalex.org/W2460533716","https://openalex.org/W2477040106","https://openalex.org/W2478601335","https://openalex.org/W2493117997","https://openalex.org/W2518007914","https://openalex.org/W2554006986","https://openalex.org/W2609684957","https://openalex.org/W2611065617","https://openalex.org/W2744050773","https://openalex.org/W2883313970","https://openalex.org/W2886474208","https://openalex.org/W2903297753","https://openalex.org/W2950034650","https://openalex.org/W2963371738","https://openalex.org/W2963589850","https://openalex.org/W2971074505","https://openalex.org/W2971247664","https://openalex.org/W2981222881","https://openalex.org/W2981656290","https://openalex.org/W3081675730","https://openalex.org/W3102533448","https://openalex.org/W3124380157","https://openalex.org/W3129604430","https://openalex.org/W3137264367","https://openalex.org/W3147886336","https://openalex.org/W3148800415","https://openalex.org/W3166566320","https://openalex.org/W4205793979","https://openalex.org/W4205815276","https://openalex.org/W4250690007","https://openalex.org/W4256055182","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2120874885","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2040975642","https://openalex.org/W2888482338","https://openalex.org/W2334254610","https://openalex.org/W4298228819","https://openalex.org/W1994623290","https://openalex.org/W1847991001","https://openalex.org/W2088165752"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2,32],"a":[3,16,53],"space-time":[4],"hybridized":[5],"discontinuous":[6],"Galerkin":[7],"method":[8],"for":[9],"the":[10,20,37,57],"evolutionary":[11],"Navier\u2013Stokes":[12],"equations":[13],"converges":[14],"to":[15,27],"weak":[17,34],"solution":[18,35],"as":[19],"time":[21],"step":[22],"and":[23,52],"mesh":[24],"size":[25],"tend":[26],"zero.":[28],"Moreover,":[29],"we":[30,44],"show":[31],"this":[33],"satisfies":[36],"energy":[38],"inequality.":[39],"To":[40],"perform":[41],"our":[42],"analysis,":[43],"make":[45],"use":[46],"of":[47,56],"discrete":[48,54],"functional":[49],"analysis":[50],"tools":[51],"version":[55],"Aubin\u2013Lions\u2013Simon":[58],"theorem.":[59]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
