{"id":"https://openalex.org/W4281777523","doi":"https://doi.org/10.1137/20m1338721","title":"Convergence of Anisotropic Mesh Adaptation via Metric Optimization","display_name":"Convergence of Anisotropic Mesh Adaptation via Metric Optimization","publication_year":2022,"publication_date":"2022-06-01","ids":{"openalex":"https://openalex.org/W4281777523","doi":"https://doi.org/10.1137/20m1338721"},"language":"en","primary_location":{"id":"doi:10.1137/20m1338721","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1338721","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/1721.1/165659","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075879904","display_name":"Hugh A. Carson","orcid":"https://orcid.org/0000-0003-1221-4850"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hugh A. Carson","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-1221-4850","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018463565","display_name":"Steven R. Allmaras","orcid":"https://orcid.org/0000-0001-7110-8949"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Steven Allmaras","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088950578","display_name":"Marshall C. Galbraith","orcid":"https://orcid.org/0000-0002-4589-7929"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marshall Galbraith","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5008751772","display_name":"David Darmofal","orcid":"https://orcid.org/0000-0001-5287-789X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David Darmofal","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-5287-789X","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5075879904"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1661,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.40773548,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"60","issue":"3","first_page":"1281","last_page":"1306"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9983000159263611,"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"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.998199999332428,"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/polygon-mesh","display_name":"Polygon mesh","score":0.7880988121032715},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6472644805908203},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6402106881141663},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5896782875061035},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5207469463348389},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5069287419319153},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4996163845062256},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4961150586605072},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.43489202857017517},{"id":"https://openalex.org/keywords/adaptive-mesh-refinement","display_name":"Adaptive mesh refinement","score":0.4227240979671478},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3499506711959839},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26253727078437805},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1482885181903839},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.10976830124855042}],"concepts":[{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.7880988121032715},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6472644805908203},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6402106881141663},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5896782875061035},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5207469463348389},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5069287419319153},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4996163845062256},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4961150586605072},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43489202857017517},{"id":"https://openalex.org/C131053463","wikidata":"https://www.wikidata.org/wiki/Q4680751","display_name":"Adaptive mesh refinement","level":2,"score":0.4227240979671478},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3499506711959839},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26253727078437805},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1482885181903839},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.10976830124855042},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","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":2,"locations":[{"id":"doi:10.1137/20m1338721","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1338721","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:dspace.mit.edu:1721.1/165659","is_oa":true,"landing_page_url":"https://hdl.handle.net/1721.1/165659","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Society for Industrial & Applied Mathematics (SIAM)","raw_type":"http://purl.org/eprint/type/JournalArticle"}],"best_oa_location":{"id":"pmh:oai:dspace.mit.edu:1721.1/165659","is_oa":true,"landing_page_url":"https://hdl.handle.net/1721.1/165659","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Society for Industrial & Applied Mathematics (SIAM)","raw_type":"http://purl.org/eprint/type/JournalArticle"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","display_name":"Climate action","score":0.5799999833106995}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W182469685","https://openalex.org/W1983496390","https://openalex.org/W1985629301","https://openalex.org/W1986964250","https://openalex.org/W1994336408","https://openalex.org/W1995404822","https://openalex.org/W1995479616","https://openalex.org/W1998050976","https://openalex.org/W1999581803","https://openalex.org/W2016094849","https://openalex.org/W2026655730","https://openalex.org/W2030604805","https://openalex.org/W2031407958","https://openalex.org/W2039924562","https://openalex.org/W2050025605","https://openalex.org/W2063277537","https://openalex.org/W2067176366","https://openalex.org/W2072811159","https://openalex.org/W2084743165","https://openalex.org/W2085850581","https://openalex.org/W2087911941","https://openalex.org/W2090807663","https://openalex.org/W2092037996","https://openalex.org/W2097944783","https://openalex.org/W2107813568","https://openalex.org/W2153245297","https://openalex.org/W2172475868","https://openalex.org/W2184367770","https://openalex.org/W2288174618","https://openalex.org/W2596456241","https://openalex.org/W2890569301","https://openalex.org/W3008009075","https://openalex.org/W3042860475","https://openalex.org/W3044774388","https://openalex.org/W3101693146"],"related_works":["https://openalex.org/W1557607869","https://openalex.org/W2366350639","https://openalex.org/W2028455732","https://openalex.org/W4313703117","https://openalex.org/W2087496541","https://openalex.org/W2108615321","https://openalex.org/W3215979663","https://openalex.org/W2020043686","https://openalex.org/W4313591746","https://openalex.org/W2147278394"],"abstract_inverted_index":{"Adaptive":[0],"finite":[1,44],"element":[2,45],"methods":[3],"(AFEMs)":[4],"are":[5],"an":[6,97],"increasingly":[7],"common":[8],"means":[9],"of":[10,18,22,39,79,89,94,107,117,125,139],"automatically":[11],"controlling":[12],"error":[13,103],"in":[14,76],"numerical":[15,134],"simulations.":[16],"Proofs":[17],"convergence":[19,23,90,126],"and":[20,53],"rate":[21,124],"exist":[24],"for":[25,36,62,91,127,142],"AFEMs;":[26],"however,":[27],"these":[28],"proofs":[29],"typically":[30],"rely":[31],"upon":[32],"a":[33,58,63,68,77,87,92,115,128,143],"nested":[34],"structure":[35],"the":[37,49,102,105,121,137,140],"sequence":[38,78,106,116],"meshes.":[40,81,108],"A":[41],"metric":[42,60],"adaptive":[43],"method":[46],"(MAFEM)":[47],"utilizes":[48],"continuous":[50],"mesh":[51,69],"model":[52],"instead":[54],"seeks":[55],"to":[56,100],"optimize":[57],"Riemannian":[59],"field":[61],"given":[64,129],"cost,":[65],"from":[66],"which":[67],"is":[70],"generated.":[71],"This":[72],"meshing":[73],"process":[74],"results":[75,135],"nonnested":[80],"In":[82,109],"this":[83],"paper":[84],"we":[85,111],"introduce":[86],"proof":[88],"class":[93],"MAFEM,":[95],"utilizing":[96],"optimization":[98],"statement":[99],"relate":[101],"on":[104],"addition,":[110],"prove":[112],"that":[113],"such":[114],"meshes":[118],"will":[119],"demonstrate":[120,136],"optimal":[122],"asymptotic":[123],"polynomial":[130],"order.":[131],"Finally":[132],"some":[133],"performance":[138],"algorithm":[141],"singularly":[144],"perturbed":[145],"linear":[146],"advection":[147],"diffusion":[148],"problem.":[149]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-28T14:05:53.105641","created_date":"2025-10-10T00:00:00"}