{"id":"https://openalex.org/W2903225406","doi":"https://doi.org/10.1137/18m1229080","title":"Some Convergence and Optimality Results of Adaptive Mixed Methods in Finite Element Exterior Calculus","display_name":"Some Convergence and Optimality Results of Adaptive Mixed Methods in Finite Element Exterior Calculus","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2903225406","doi":"https://doi.org/10.1137/18m1229080","mag":"2903225406"},"language":"en","primary_location":{"id":"doi:10.1137/18m1229080","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1229080","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1811.11143","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045601277","display_name":"Yuwen Li","orcid":"https://orcid.org/0000-0002-4071-8653"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yuwen Li","raw_affiliation_strings":["Department of Mathematics, University of California San Diego, La Jolla, California 92093-0112"],"raw_orcid":"https://orcid.org/0000-0002-4071-8653","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California San Diego, La Jolla, California 92093-0112","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5045601277"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":1.5548,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.77910646,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"57","issue":"4","first_page":"2019","last_page":"2042"},"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":0.9936000108718872,"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/mathematics","display_name":"Mathematics","score":0.8758786916732788},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7319316267967224},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6179493069648743},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5369505882263184},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.5329405069351196},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5135560035705566},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5085726976394653},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.48387205600738525},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4740932881832123},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.46384480595588684},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.39523425698280334},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.378546804189682},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2969050407409668}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8758786916732788},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7319316267967224},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6179493069648743},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5369505882263184},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.5329405069351196},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5135560035705566},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5085726976394653},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.48387205600738525},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4740932881832123},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.46384480595588684},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.39523425698280334},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.378546804189682},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2969050407409668},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"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:10.1137/18m1229080","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1229080","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:1811.11143","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.11143","pdf_url":"https://arxiv.org/pdf/1811.11143","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,"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:1811.11143","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.11143","pdf_url":"https://arxiv.org/pdf/1811.11143","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,"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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W136185420","https://openalex.org/W1978687734","https://openalex.org/W1983072269","https://openalex.org/W1987628609","https://openalex.org/W1993064848","https://openalex.org/W1995479616","https://openalex.org/W2009985306","https://openalex.org/W2016124790","https://openalex.org/W2016365515","https://openalex.org/W2017976561","https://openalex.org/W2021411519","https://openalex.org/W2024326406","https://openalex.org/W2039924562","https://openalex.org/W2043594669","https://openalex.org/W2044959876","https://openalex.org/W2049646932","https://openalex.org/W2051682834","https://openalex.org/W2062618977","https://openalex.org/W2064909895","https://openalex.org/W2065479689","https://openalex.org/W2067802257","https://openalex.org/W2071036364","https://openalex.org/W2072811159","https://openalex.org/W2079386274","https://openalex.org/W2084743165","https://openalex.org/W2089768471","https://openalex.org/W2095044295","https://openalex.org/W2107813568","https://openalex.org/W2118551467","https://openalex.org/W2138486270","https://openalex.org/W2157121531","https://openalex.org/W2169143985","https://openalex.org/W2196858524","https://openalex.org/W2262198896","https://openalex.org/W2577596286","https://openalex.org/W2594541596","https://openalex.org/W2903553401","https://openalex.org/W2906022956","https://openalex.org/W2963458162","https://openalex.org/W2964048411","https://openalex.org/W3020145752","https://openalex.org/W3103476862","https://openalex.org/W4232765720","https://openalex.org/W4245007249"],"related_works":["https://openalex.org/W3185235544","https://openalex.org/W4297791327","https://openalex.org/W2897842840","https://openalex.org/W2911623553","https://openalex.org/W4387559320","https://openalex.org/W188518547","https://openalex.org/W2362625355","https://openalex.org/W2020718081","https://openalex.org/W4390806324","https://openalex.org/W4376312451"],"abstract_inverted_index":{"In":[0,46],"this":[1],"paper,":[2],"we":[3,48],"present":[4],"several":[5],"new":[6],"a":[7],"posteriori":[8],"error":[9],"estimators":[10],"and":[11,19,35,68,74],"two":[12],"adaptive":[13],"mixed":[14],"finite":[15,27],"element":[16,28],"methods":[17],"AMFEM1":[18,34],"AMFEM2":[20,36],"for":[21,77],"the":[22,50,70,78],"Hodge":[23,79],"Laplacian":[24],"problem":[25],"in":[26],"exterior":[29],"calculus.":[30],"We":[31],"prove":[32,49],"that":[33],"are":[37],"both":[38],"convergent":[39],"starting":[40],"from":[41],"any":[42],"initial":[43],"coarse":[44],"mesh.":[45],"addition,":[47],"quasi-optimality":[51,75],"of":[52],"AMFEM2.":[53],"As":[54],"opposed":[55],"to":[56],"existing":[57],"literature,":[58],"our":[59],"results":[60,76],"work":[61],"on":[62],"Lipschitz":[63],"domains":[64],"with":[65],"nontrivial":[66],"cohomology":[67],"provide":[69],"first":[71],"norm":[72],"convergence":[73],"Laplacian.":[80]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
