{"id":"https://openalex.org/W7213240269","doi":"https://doi.org/10.48550/arxiv.2609.15223","title":"Structure-Preserving Augmented Lagrangian Finite Element Methods for Cavitation in Reynolds and Stokes Flows","display_name":"Structure-Preserving Augmented Lagrangian Finite Element Methods for Cavitation in Reynolds and Stokes Flows","publication_year":2026,"publication_date":"2026-09-14","ids":{"openalex":"https://openalex.org/W7213240269","doi":"https://doi.org/10.48550/arxiv.2609.15223"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.15223","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15223","pdf_url":"https://arxiv.org/pdf/2609.15223","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/2609.15223","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016292096","display_name":"Peter Hansbo","orcid":"https://orcid.org/0000-0001-7352-1550","observed_orcids":["https://orcid.org/0000-0001-7352-1550"]},"institutions":[{"id":"https://openalex.org/I94616838","display_name":"J\u00f6nk\u00f6ping University","ror":"https://ror.org/03t54am93","country_code":"SE","type":"education","lineage":["https://openalex.org/I94616838"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Hansbo, Peter","raw_affiliation_strings":["Department of Mechanical Engineering , J\u00f6nk\u00f6ping University , SE-55111 J\u00f6nk\u00f6ping , Sweden,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering , J\u00f6nk\u00f6ping University , SE-55111 J\u00f6nk\u00f6ping , Sweden,","institution_ids":["https://openalex.org/I94616838"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077614976","display_name":"Mats G. Larson","orcid":"https://orcid.org/0000-0001-5589-4521","observed_orcids":["https://orcid.org/0000-0001-5589-4521"]},"institutions":[{"id":"https://openalex.org/I90267481","display_name":"Ume\u00e5 University","ror":"https://ror.org/05kb8h459","country_code":"SE","type":"education","lineage":["https://openalex.org/I90267481"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Larson, Mats G.","raw_affiliation_strings":["Department of Mathematics and Mathematical Statistics , Ume\u00e5 University , SE-901 87 Ume\u00e5 , Sweden,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Mathematical Statistics , Ume\u00e5 University , SE-901 87 Ume\u00e5 , Sweden,","institution_ids":["https://openalex.org/I90267481"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"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":0.9887999892234802,"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":0.9887999892234802,"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/T11138","display_name":"Tribology and Lubrication Engineering","score":0.006300000008195639,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.0008999999845400453,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cavitation","display_name":"cavitation","score":0.9549999833106995},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"augmented Lagrangian method","score":0.7820000052452087},{"id":"https://openalex.org/keywords/reynolds-equation","display_name":"Reynolds equation","score":0.847000002861023},{"id":"https://openalex.org/keywords/stokes-flow","display_name":"Stokes flow","score":0.9409999847412109},{"id":"https://openalex.org/keywords/lubrication","display_name":"lubrication","score":0.7110000252723694},{"id":"https://openalex.org/keywords/complementarity-conditions","display_name":"complementarity conditions","score":0.699999988079071},{"id":"https://openalex.org/keywords/crouzeix-raviart-element","display_name":"Crouzeix-Raviart element","score":0.8960000276565552},{"id":"https://openalex.org/keywords/error-estimates","display_name":"error estimates","score":0.6940000057220459},{"id":"https://openalex.org/keywords/well-posedness","display_name":"well-posedness","score":0.847000002861023},{"id":"https://openalex.org/keywords/stability-threshold","display_name":"stability threshold","score":0.8040000200271606},{"id":"https://openalex.org/keywords/deviatoric-stress","display_name":"deviatoric stress","score":0.7350000143051147},{"id":"https://openalex.org/keywords/pressure-profile","display_name":"pressure profile","score":0.3269999921321869}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7003999948501587},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6013000011444092},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.588699996471405},{"id":"https://openalex.org/C182748727","wikidata":"https://www.wikidata.org/wiki/Q178932","display_name":"Reynolds number","level":3,"score":0.5806999802589417},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5752999782562256},{"id":"https://openalex.org/C207057113","wikidata":"https://www.wikidata.org/wiki/Q201666","display_name":"Cavitation","level":2,"score":0.5554999709129333},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5371999740600586},{"id":"https://openalex.org/C32526432","wikidata":"https://www.wikidata.org/wiki/Q1536235","display_name":"Reynolds-averaged Navier\u2013Stokes equations","level":3,"score":0.5278000235557556},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.47209998965263367},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.415800005197525},{"id":"https://openalex.org/C21018558","wikidata":"https://www.wikidata.org/wiki/Q7241680","display_name":"Pressure-correction method","level":3,"score":0.3986000120639801},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.38760000467300415},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.3619999885559082},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.36149999499320984},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.3598000109195709},{"id":"https://openalex.org/C19191322","wikidata":"https://www.wikidata.org/wiki/Q674202","display_name":"Stokes flow","level":3,"score":0.358599990606308},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.35350000858306885},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3490000069141388},{"id":"https://openalex.org/C157334427","wikidata":"https://www.wikidata.org/wiki/Q7319639","display_name":"Reynolds equation","level":4,"score":0.34279999136924744},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.3172999918460846},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.30720001459121704},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.29789999127388},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.2851000130176544},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2775000035762787},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.2703000009059906}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.15223","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15223","pdf_url":"https://arxiv.org/pdf/2609.15223","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.2609.15223","doi":"https://doi.org/10.48550/arxiv.2609.15223","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.15223","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","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:2609.15223","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15223","pdf_url":"https://arxiv.org/pdf/2609.15223","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213240269.pdf","grobid_xml":"https://content.openalex.org/works/W7213240269.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4407012640","https://openalex.org/W7126051100","https://openalex.org/W7204955079"],"related_works":["https://openalex.org/W2769490231","https://openalex.org/W2022540470","https://openalex.org/W2138265224","https://openalex.org/W4387425037","https://openalex.org/W1897390446","https://openalex.org/W1974461496","https://openalex.org/W2018363384","https://openalex.org/W7117536897","https://openalex.org/W3132170461","https://openalex.org/W4392922612"],"abstract_inverted_index":{"In":[0],"this":[1,41],"paper":[2],"we":[3,54,76],"propose":[4],"augmented":[5],"Lagrangian":[6],"finite":[7],"element":[8,109],"methods":[9],"for":[10,20,52],"cavitation":[11],"in":[12,46,118,142],"the":[13,22,29,35,38,56,64,79,83,87,99,143,152,158,162],"Reynolds":[14,39],"and":[15,28,110,114,120,123,136],"Stokes":[16,74],"models":[17,145],"of":[18,34,68,161],"lubrication,":[19],"which":[21,53,132],"discrete":[23],"complementarity":[24],"conditions":[25,160],"hold":[26],"exactly":[27],"augmentation":[30],"parameter":[31],"drops":[32],"out":[33],"method.":[36],"For":[37,73],"equation":[40],"follows":[42],"from":[43],"nodal":[44],"quadrature":[45],"a":[47,69,106,124],"mixed":[48],"piecewise":[49,111],"linear":[50],"method,":[51],"prove":[55,115],"classical":[57],"first-order":[58,125],"error":[59,126],"estimate.":[60,127],"We":[61,103,128],"also":[62,154],"determine":[63],"computable":[65],"stability":[66,117],"threshold":[67],"multiplier-free":[70],"stabilised":[71],"alternative.":[72],"flow":[75],"show":[77,137],"that":[78,138],"constrained":[80],"scalar":[81],"is":[82,94],"mechanical":[84],"pressure":[85,140],"when":[86],"deviatoric":[88],"stress,":[89],"with":[90,98,105],"zero":[91],"bulk":[92],"viscosity,":[93],"used,":[95],"but":[96],"not":[97,147],"customary":[100],"incompressible":[101],"stress.":[102],"discretise":[104],"jump-stabilised":[107],"Crouzeix-Raviart":[108],"constant":[112],"pressure,":[113],"well-posedness,":[116],"two":[119,144],"three":[121],"dimensions,":[122],"present":[129],"numerical":[130],"examples":[131],"verify":[133],"these":[134],"properties":[135],"close":[139,149],"profiles":[141],"do":[146],"imply":[148],"cavity":[150],"predictions,":[151],"latter":[153],"being":[155],"sensitive":[156],"to":[157],"end":[159],"computational":[163],"domain.":[164]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-16T00:00:00"}
