{"id":"https://openalex.org/W2427508275","doi":"https://doi.org/10.1137/16m1080495","title":"Variational Formulation and Numerical Analysis of Linear Elliptic Equations in Nondivergence form with Cordes Coefficients","display_name":"Variational Formulation and Numerical Analysis of Linear Elliptic Equations in Nondivergence form with Cordes Coefficients","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2427508275","doi":"https://doi.org/10.1137/16m1080495","mag":"2427508275"},"language":"en","primary_location":{"id":"doi:10.1137/16m1080495","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1080495","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/1606.05631","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035829145","display_name":"Dietmar Gallistl","orcid":"https://orcid.org/0000-0001-8954-4175"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Dietmar Gallistl","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5035829145"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.00422682,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"55","issue":"2","first_page":"737","last_page":"757"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9986000061035156,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9983999729156494,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7604951858520508},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6935521960258484},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.656833291053772},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5780874490737915},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.5654470920562744},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.5487240552902222},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5366935133934021},{"id":"https://openalex.org/keywords/isogeometric-analysis","display_name":"Isogeometric analysis","score":0.5171312689781189},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.5024521350860596},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.471781462430954},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4100790023803711},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.350200891494751},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34548839926719666},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14391160011291504},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10387492179870605},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07316789031028748}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7604951858520508},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6935521960258484},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.656833291053772},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5780874490737915},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.5654470920562744},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.5487240552902222},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5366935133934021},{"id":"https://openalex.org/C2780737243","wikidata":"https://www.wikidata.org/wiki/Q17082433","display_name":"Isogeometric analysis","level":3,"score":0.5171312689781189},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.5024521350860596},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.471781462430954},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4100790023803711},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.350200891494751},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34548839926719666},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14391160011291504},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10387492179870605},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07316789031028748},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/16m1080495","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1080495","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:1606.05631","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1606.05631","pdf_url":"https://arxiv.org/pdf/1606.05631","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":null,"raw_type":"text"},{"id":"mag:2427508275","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1606.05631.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.1606.05631","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1606.05631","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:1606.05631","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1606.05631","pdf_url":"https://arxiv.org/pdf/1606.05631","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5106512922","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6024419964","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6052429835","display_name":null,"funder_award_id":"(DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8666300730","display_name":null,"funder_award_id":"CRC1173","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2427508275.pdf","grobid_xml":"https://content.openalex.org/works/W2427508275.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1586623601","https://openalex.org/W1872227664","https://openalex.org/W1972877576","https://openalex.org/W1987461346","https://openalex.org/W2038580008","https://openalex.org/W2039924562","https://openalex.org/W2077040879","https://openalex.org/W2084743165","https://openalex.org/W2090255516","https://openalex.org/W2091450899","https://openalex.org/W2169143985","https://openalex.org/W2522501703","https://openalex.org/W3102092453","https://openalex.org/W4231670924"],"related_works":["https://openalex.org/W2963227054","https://openalex.org/W2479238691","https://openalex.org/W2050981166","https://openalex.org/W2047382066","https://openalex.org/W2155126547","https://openalex.org/W2987600563","https://openalex.org/W2322007186","https://openalex.org/W2076458295","https://openalex.org/W2265696467","https://openalex.org/W2105267569","https://openalex.org/W2899272800","https://openalex.org/W2894737583","https://openalex.org/W2288779909","https://openalex.org/W1805223829","https://openalex.org/W2894415323","https://openalex.org/W2281275892","https://openalex.org/W2191632485","https://openalex.org/W2044440399","https://openalex.org/W2971784646","https://openalex.org/W149982730"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"formulations":[3,52],"of":[4,25,56,66,78,106],"second-order":[5],"elliptic":[6],"partial":[7],"differential":[8],"equations":[9],"in":[10,64],"nondivergence":[11],"form":[12],"on":[13,47,114],"convex":[14],"domains":[15],"as":[16,68,70],"equivalent":[17],"variational":[18,62,90],"problems.":[19],"The":[20,104],"first":[21],"formulation":[22,45],"is":[23,41,110],"that":[24],"Smears":[26],"and":[27,37,101,116],"S\u00fcli":[28],"[SIAM":[29],"J.":[30],"Numer.":[31],"Anal.,":[32],"51":[33],"(2013),":[34],"pp.":[35],"2088--2106],":[36],"the":[38,54,76,82,89],"second":[39],"one":[40],"a":[42,48,85,94],"new":[43],"symmetric":[44],"based":[46],"least-squares":[49],"functional.":[50],"These":[51],"enable":[53],"use":[55],"standard":[57],"finite":[58,72],"element":[59,73],"techniques":[60],"for":[61,93],"problems":[63],"subspaces":[65],"$H^2$":[67],"well":[69],"mixed":[71],"methods":[74],"from":[75],"context":[77],"fluid":[79],"computations.":[80],"Besides":[81],"immediate":[83],"quasi-optimal":[84],"priori":[86],"error":[87,96],"bounds,":[88],"setting":[91],"allows":[92],"posteriori":[95],"control":[97],"with":[98],"explicit":[99],"constants":[100],"adaptive":[102,108,117],"mesh-refinement.":[103],"convergence":[105],"an":[107],"algorithm":[109],"proved.":[111],"Numerical":[112],"results":[113],"uniform":[115],"meshes":[118],"are":[119],"included.":[120]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}
