{"id":"https://openalex.org/W3049386309","doi":"https://doi.org/10.1137/20m1360098","title":"Divergence-free Scott--Vogelius Elements on Curved Domains","display_name":"Divergence-free Scott--Vogelius Elements on Curved Domains","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3049386309","doi":"https://doi.org/10.1137/20m1360098","mag":"3049386309"},"language":"en","primary_location":{"id":"doi:10.1137/20m1360098","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1360098","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2008.06429","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039552338","display_name":"Michael Neilan","orcid":"https://orcid.org/0000-0002-1564-1041"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Michael Neilan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5089504569","display_name":"M. Baris Otus","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Baris Otus","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039552338"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00809784,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"59","issue":"2","first_page":"1090","last_page":"1116"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9993000030517578,"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/T10514","display_name":"Numerical methods in engineering","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/divergence","display_name":"Divergence (linguistics)","score":0.7427977323532104},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7299327850341797},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.6317952871322632},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5865901708602905},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.574937641620636},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5136470198631287},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.5007846355438232},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48340073227882385},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.45911306142807007},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.41835296154022217},{"id":"https://openalex.org/keywords/extended-finite-element-method","display_name":"Extended finite element method","score":0.4179675579071045},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41487917304039},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39569708704948425},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24536550045013428},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20207050442695618},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18687891960144043},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.052741438150405884}],"concepts":[{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.7427977323532104},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7299327850341797},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.6317952871322632},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5865901708602905},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.574937641620636},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5136470198631287},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.5007846355438232},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48340073227882385},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.45911306142807007},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.41835296154022217},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.4179675579071045},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41487917304039},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39569708704948425},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24536550045013428},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20207050442695618},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18687891960144043},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.052741438150405884},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1360098","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1360098","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2008.06429","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2008.06429","pdf_url":"https://arxiv.org/pdf/2008.06429","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":"","raw_type":"text"},{"id":"mag:3049386309","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/2008.06429.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2008.06429","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2008.06429","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2008.06429","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2008.06429","pdf_url":"https://arxiv.org/pdf/2008.06429","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":"","raw_type":"text"},"sustainable_development_goals":[{"score":0.6200000047683716,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G1471342941","display_name":null,"funder_award_id":"DMS-2011733","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3049386309.pdf","grobid_xml":"https://content.openalex.org/works/W3049386309.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W107777212","https://openalex.org/W1582734821","https://openalex.org/W1799147386","https://openalex.org/W1928567235","https://openalex.org/W1972683041","https://openalex.org/W1973212083","https://openalex.org/W2008635392","https://openalex.org/W2012437014","https://openalex.org/W2032833911","https://openalex.org/W2039279171","https://openalex.org/W2041523977","https://openalex.org/W2044270153","https://openalex.org/W2059975982","https://openalex.org/W2068064731","https://openalex.org/W2087240734","https://openalex.org/W2160623568","https://openalex.org/W2195937117","https://openalex.org/W2744050773","https://openalex.org/W2962917950","https://openalex.org/W2963131956","https://openalex.org/W2998796568"],"related_works":["https://openalex.org/W3158636760","https://openalex.org/W587519822","https://openalex.org/W74748254","https://openalex.org/W2949987265","https://openalex.org/W2305531518","https://openalex.org/W2156629649","https://openalex.org/W1967936314","https://openalex.org/W2290810370","https://openalex.org/W2253555957","https://openalex.org/W2683415073","https://openalex.org/W2887442002","https://openalex.org/W2283070814","https://openalex.org/W2058111044","https://openalex.org/W141078179","https://openalex.org/W2002366046","https://openalex.org/W2079078229","https://openalex.org/W1522875489","https://openalex.org/W3182374780","https://openalex.org/W3121829928","https://openalex.org/W2972839478"],"abstract_inverted_index":{"We":[0,63],"construct":[1],"and":[2,47,75],"analyze":[3],"an":[4],"isoparametric":[5],"finite":[6,24,44],"element":[7,25,45],"pair":[8,17,56],"for":[9],"the":[10,22,35,41,49,54,58,61,66,85],"Stokes":[11],"problem":[12],"in":[13,57],"two":[14],"dimensions.":[15],"The":[16,31],"is":[18,73,76],"defined":[19],"by":[20],"mapping":[21],"Scott-Vogelius":[23,55],"space":[26,33],"via":[27],"a":[28],"Piola":[29],"transform.":[30],"velocity":[32],"has":[34],"same":[36],"degrees":[37],"of":[38,60],"freedom":[39],"as":[40],"quadratic":[42],"Lagrange":[43],"space,":[46],"therefore":[48],"proposed":[50],"spaces":[51],"reduce":[52],"to":[53],"interior":[59],"domain.":[62],"prove":[64],"that":[65],"resulting":[67],"method":[68],"converges":[69],"with":[70],"optimal":[71],"order,":[72],"divergence--free,":[74],"pressure":[77],"robust.":[78],"Numerical":[79],"examples":[80],"are":[81],"provided":[82],"which":[83],"support":[84],"theoretical":[86],"results.":[87]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
