{"id":"https://openalex.org/W2964204805","doi":"https://doi.org/10.1137/20m1335613","title":"Adaptive Morley FEM for the von K\u00e1rm\u00e1n Equations with Optimal Convergence Rates","display_name":"Adaptive Morley FEM for the von K\u00e1rm\u00e1n Equations with Optimal Convergence Rates","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W2964204805","doi":"https://doi.org/10.1137/20m1335613","mag":"2964204805"},"language":"en","primary_location":{"id":"doi:10.1137/20m1335613","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1335613","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036808184","display_name":"Carsten Carstensen","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Carsten Carstensen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5019365126","display_name":"Neela Nataraj","orcid":"https://orcid.org/0000-0002-5180-459X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Neela Nataraj","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036808184"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1363,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.85307242,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"59","issue":"2","first_page":"696","last_page":"719"},"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":1.0,"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":1.0,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994000196456909,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8660935163497925},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.707856297492981},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.699272632598877},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6457004547119141},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.6064016819000244},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5548683404922485},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5334919095039368},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4894620180130005},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.47595450282096863},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.45047104358673096},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.4246251583099365},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42016273736953735},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.41868600249290466},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35486307740211487},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.21946343779563904},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11342918872833252},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08864504098892212}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8660935163497925},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.707856297492981},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.699272632598877},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6457004547119141},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.6064016819000244},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5548683404922485},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5334919095039368},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4894620180130005},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.47595450282096863},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.45047104358673096},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4246251583099365},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42016273736953735},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.41868600249290466},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35486307740211487},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.21946343779563904},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11342918872833252},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08864504098892212},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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":1,"locations":[{"id":"doi:10.1137/20m1335613","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1335613","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5448639614","display_name":null,"funder_award_id":"CA 151/22-2","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G648484195","display_name":null,"funder_award_id":"MTR/2017/000199","funder_id":"https://openalex.org/F4320334771","funder_display_name":"Science and Engineering Research Board"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320330412","display_name":"Scheme for Promotion of Academic and Research Collaboration","ror":null},{"id":"https://openalex.org/F4320334771","display_name":"Science and Engineering Research Board","ror":"https://ror.org/03ffdsr55"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W21295503","https://openalex.org/W1972502206","https://openalex.org/W1973103891","https://openalex.org/W1983733848","https://openalex.org/W1988641610","https://openalex.org/W2002410282","https://openalex.org/W2012900529","https://openalex.org/W2019685695","https://openalex.org/W2026409663","https://openalex.org/W2031815655","https://openalex.org/W2044959876","https://openalex.org/W2048407683","https://openalex.org/W2054401206","https://openalex.org/W2058363312","https://openalex.org/W2072811159","https://openalex.org/W2074282379","https://openalex.org/W2084743165","https://openalex.org/W2092037996","https://openalex.org/W2095197130","https://openalex.org/W2107813568","https://openalex.org/W2110176271","https://openalex.org/W2172266329","https://openalex.org/W2179536916","https://openalex.org/W2298572172","https://openalex.org/W2462781348","https://openalex.org/W2552077385","https://openalex.org/W2765080741","https://openalex.org/W2962713585","https://openalex.org/W2963175427","https://openalex.org/W2963483775","https://openalex.org/W3004866040","https://openalex.org/W3021640518","https://openalex.org/W3102639848"],"related_works":["https://openalex.org/W2164189677","https://openalex.org/W2133947431","https://openalex.org/W2490196280","https://openalex.org/W3182827720","https://openalex.org/W1596838019","https://openalex.org/W3208509670","https://openalex.org/W2109304297","https://openalex.org/W2100864966","https://openalex.org/W2083709218","https://openalex.org/W4323366562"],"abstract_inverted_index":{"The":[0,81,98],"adaptive":[1],"nonconforming":[2,79],"Morley":[3,92],"finite":[4],"element":[5],"method":[6],"approximates":[7],"a":[8,86,103,107,112],"regular":[9],"solution":[10],"to":[11],"the":[12,29,35,40,60,63,69,74,78,90,95,116],"von":[13],"K\u00e1rm\u00e1n":[14],"equations":[15],"with":[16,39,85],"optimal":[17],"convergence":[18],"rates":[19],"for":[20,89],"sufficiently":[21],"fine":[22],"triangulations":[23],"and":[24,48,62,111],"small":[25],"bulk":[26],"parameter":[27],"in":[28,68,73],"D\u00f6rfler":[30],"marking.":[31],"This":[32],"follows":[33,84],"from":[34,94],"general":[36],"axiomatic":[37],"framework":[38],"key":[41],"arguments":[42],"of":[43,50,77,115],"stability,":[44],"reduction,":[45],"discrete":[46,82,91],"reliability,":[47],"quasiorthogonality":[49,99],"an":[51],"explicit":[52],"residual-based":[53],"error":[54,109],"estimator.":[55],"Particular":[56],"attention":[57],"is":[58],"on":[59,102],"nonlinearity":[61],"piecewise":[64,105],"Sobolev":[65],"embeddings":[66],"required":[67],"resulting":[70],"trilinear":[71],"form":[72],"weak":[75],"formulation":[76],"discretization.":[80],"reliability":[83],"conforming":[87],"companion":[88],"functions":[93],"medius":[96],"analysis.":[97],"also":[100],"relies":[101],"novel":[104],"$H^1$":[106],"priori":[108],"estimate":[110],"careful":[113],"analysis":[114],"nonlinearity.":[117]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}