{"id":"https://openalex.org/W3138374136","doi":"https://doi.org/10.1137/21m1407495","title":"Gamma-Convergent Projection-Free Finite Element Methods for Nematic Liquid Crystals: The Ericksen Model","display_name":"Gamma-Convergent Projection-Free Finite Element Methods for Nematic Liquid Crystals: The Ericksen Model","publication_year":2022,"publication_date":"2022-04-01","ids":{"openalex":"https://openalex.org/W3138374136","doi":"https://doi.org/10.1137/21m1407495","mag":"3138374136"},"language":"en","primary_location":{"id":"doi:10.1137/21m1407495","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1407495","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hdl.handle.net/11585/944078","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040883953","display_name":"Ricardo H. Nochetto","orcid":"https://orcid.org/0009-0002-8895-1144"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ricardo H. Nochetto","raw_affiliation_strings":["University of Maryland, Department of Mathematics and Institute for Physical Science and Technology, College Park, MD 20742, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Maryland, Department of Mathematics and Institute for Physical Science and Technology, College Park, MD 20742, USA","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059625967","display_name":"Michele Ruggeri","orcid":"https://orcid.org/0000-0001-6213-1602"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Michele Ruggeri","raw_affiliation_strings":["TU Wien, Institute of Analysis and Scientific Computing, 1040 Vienna, Austria"],"raw_orcid":"https://orcid.org/0000-0001-6213-1602","affiliations":[{"raw_affiliation_string":"TU Wien, Institute of Analysis and Scientific Computing, 1040 Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101788472","display_name":"Shuo Yang","orcid":"https://orcid.org/0000-0001-9085-5085"},"institutions":[{"id":"https://openalex.org/I4403928416","display_name":"Beijing Institute of Mathematical Sciences and Applications","ror":"https://ror.org/05t6hvr95","country_code":null,"type":"education","lineage":["https://openalex.org/I4403928416","https://openalex.org/I99065089"]},{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuo Yang","raw_affiliation_strings":["Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, 101408 Beijing, China, and Yau Mathematical Sciences Center,","Tsinghua University, 100084 Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, 101408 Beijing, China, and Yau Mathematical Sciences Center,","institution_ids":["https://openalex.org/I4403928416"]},{"raw_affiliation_string":"Tsinghua University, 100084 Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5040883953"],"corresponding_institution_ids":["https://openalex.org/I66946132"],"apc_list":null,"apc_paid":null,"fwci":0.1219,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.26874617,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"60","issue":"2","first_page":"856","last_page":"887"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10306","display_name":"Liquid Crystal Research Advancements","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10306","display_name":"Liquid Crystal Research Advancements","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11737","display_name":"Advanced Materials and Mechanics","score":0.996399998664856,"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/T12405","display_name":"Characterization and Applications of Magnetic Nanoparticles","score":0.9861000180244446,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/finite-element-method","display_name":"Finite element method","score":0.7610337734222412},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7019890546798706},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.6811650991439819},{"id":"https://openalex.org/keywords/liquid-crystal","display_name":"Liquid crystal","score":0.6481623649597168},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5688953399658203},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5342943072319031},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48570284247398376},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.46048980951309204},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.45988428592681885},{"id":"https://openalex.org/keywords/scalar-field","display_name":"Scalar field","score":0.44860365986824036},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4310660660266876},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.27217966318130493},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23540708422660828},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17325827479362488},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.0926189124584198}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7610337734222412},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7019890546798706},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.6811650991439819},{"id":"https://openalex.org/C13274807","wikidata":"https://www.wikidata.org/wiki/Q203989","display_name":"Liquid crystal","level":2,"score":0.6481623649597168},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5688953399658203},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5342943072319031},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48570284247398376},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.46048980951309204},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.45988428592681885},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.44860365986824036},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4310660660266876},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27217966318130493},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23540708422660828},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17325827479362488},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0926189124584198},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"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/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":3,"locations":[{"id":"doi:10.1137/21m1407495","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1407495","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:strathprints.strath.ac.uk:80266","is_oa":false,"landing_page_url":"https://strathprints.strath.ac.uk/view/author/1378929.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4306402226","display_name":"Strathprints: The University of Strathclyde institutional repository (University of Strathclyde)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I181647926","host_organization_name":"University of Strathclyde","host_organization_lineage":["https://openalex.org/I181647926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:cris.unibo.it:11585/944078","is_oa":true,"landing_page_url":"https://hdl.handle.net/11585/944078","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:cris.unibo.it:11585/944078","is_oa":true,"landing_page_url":"https://hdl.handle.net/11585/944078","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1786514303","display_name":null,"funder_award_id":"DMS-1439786","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3066556971","display_name":null,"funder_award_id":"DMS-1908267","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7198856295","display_name":null,"funder_award_id":"1908267","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"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320321692","display_name":"Erwin Schr\u00f6dinger International Institute for Mathematics and Physics","ror":"https://ror.org/03prydq77"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W418503264","https://openalex.org/W1498712972","https://openalex.org/W1561385072","https://openalex.org/W1569061876","https://openalex.org/W1600845614","https://openalex.org/W1968731434","https://openalex.org/W1977708589","https://openalex.org/W1998532591","https://openalex.org/W2015660465","https://openalex.org/W2019798593","https://openalex.org/W2027667809","https://openalex.org/W2029449803","https://openalex.org/W2035427049","https://openalex.org/W2039925534","https://openalex.org/W2045933447","https://openalex.org/W2056828987","https://openalex.org/W2058578329","https://openalex.org/W2124673822","https://openalex.org/W2146329425","https://openalex.org/W2232537544","https://openalex.org/W2333025053","https://openalex.org/W2745124834","https://openalex.org/W2964831957","https://openalex.org/W2996234610","https://openalex.org/W3037733829","https://openalex.org/W3042898385","https://openalex.org/W3091871338","https://openalex.org/W3105714921"],"related_works":["https://openalex.org/W1557607869","https://openalex.org/W2366350639","https://openalex.org/W2018289167","https://openalex.org/W2069570482","https://openalex.org/W2080612831","https://openalex.org/W2018581211","https://openalex.org/W2028455732","https://openalex.org/W4323274447","https://openalex.org/W3012684067","https://openalex.org/W1970712301"],"abstract_inverted_index":{"The":[0],"Ericksen":[1],"model":[2],"for":[3,76,102],"nematic":[4],"liquid":[5],"crystals":[6],"couples":[7],"a":[8,12,30],"director":[9],"field":[10],"with":[11,25],"scalar":[13],"degree":[14],"of":[15,22,37,59,84,91,109,113,129],"orientation":[16],"variable":[17],"and":[18,54,81,122,133],"allows":[19],"the":[20,38,57,85,89,107,110,114,127,130],"formation":[21],"various":[23],"defects":[24],"finite":[26,34,47],"energy.":[27],"We":[28,78,93,116],"propose":[29],"simple":[31],"but":[32,70],"novel":[33],"element":[35,48],"approximation":[36],"problem":[39],"that":[40,105,125],"can":[41],"be":[42],"implemented":[43],"easily":[44],"within":[45],"standard":[46],"packages.":[49],"Our":[50],"scheme":[51,132],"is":[52],"projection-free":[53],"thus":[55],"circumvents":[56],"use":[58],"weakly":[60],"acute":[61],"meshes,":[62],"which":[63],"are":[64,71],"quite":[65,138],"restrictive":[66],"in":[67,88,120],"three":[68,123],"dimensions":[69,124],"required":[72],"by":[73],"recent":[74],"algorithms":[75],"convergence.":[77],"prove":[79],"stability":[80],"$\\Gamma$-convergence":[82],"properties":[83],"new":[86],"method":[87],"presence":[90],"defects.":[92,140],"also":[94],"design":[95],"an":[96],"effective":[97],"nested":[98],"gradient":[99],"flow":[100],"algorithm":[101],"computing":[103],"minimizers":[104],"controls":[106],"violation":[108],"unit-length":[111],"constraint":[112],"director.":[115],"present":[117],"several":[118],"simulations":[119],"two":[121],"document":[126],"performance":[128],"proposed":[131],"its":[134],"ability":[135],"to":[136],"capture":[137],"intriguing":[139]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-04-24T08:23:43.765630","created_date":"2021-03-29T00:00:00"}