{"id":"https://openalex.org/W2038580008","doi":"https://doi.org/10.1137/100787672","title":"A Finite Element Method for Second Order Nonvariational Elliptic Problems","display_name":"A Finite Element Method for Second Order Nonvariational Elliptic Problems","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2038580008","doi":"https://doi.org/10.1137/100787672","mag":"2038580008"},"language":"en","primary_location":{"id":"doi:10.1137/100787672","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100787672","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1003.0292","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Omar Lakkis","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Omar Lakkis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Tristan Pryer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tristan Pryer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.252,"has_fulltext":true,"cited_by_count":40,"citation_normalized_percentile":{"value":0.78966089,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"33","issue":"2","first_page":"786","last_page":"801"},"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":0.6230000257492065,"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":0.6230000257492065,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.13339999318122864,"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":0.08250000327825546,"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/finite-element-method","display_name":"Finite element method","score":0.7172999978065491},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.63919997215271},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.5957000255584717},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5755000114440918},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.45820000767707825},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.44119998812675476},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.38749998807907104},{"id":"https://openalex.org/keywords/numerical-linear-algebra","display_name":"Numerical linear algebra","score":0.38749998807907104},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.3874000012874603}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7965999841690063},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7172999978065491},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.63919997215271},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.5957000255584717},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5755000114440918},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4733000099658966},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.45820000767707825},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4458000063896179},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.44119998812675476},{"id":"https://openalex.org/C163834973","wikidata":"https://www.wikidata.org/wiki/Q2004891","display_name":"Numerical linear algebra","level":3,"score":0.38749998807907104},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.38749998807907104},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3874000012874603},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.37439998984336853},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.33059999346733093},{"id":"https://openalex.org/C201801670","wikidata":"https://www.wikidata.org/wiki/Q2132775","display_name":"Elliptic rational functions","level":4,"score":0.31040000915527344},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.3084000051021576},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.30550000071525574},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.30160000920295715},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2978000044822693},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.2815999984741211},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.28029999136924744},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C3161131","wikidata":"https://www.wikidata.org/wiki/Q14097093","display_name":"Linear elasticity","level":3,"score":0.2583000063896179},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2517000138759613}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/100787672","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100787672","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:centaur.reading.ac.uk:33812","is_oa":false,"landing_page_url":"https://centaur.reading.ac.uk/view/creators/90005524.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4306402273","display_name":"CentAUR (University of Reading)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71052956","host_organization_name":"University of Reading","host_organization_lineage":["https://openalex.org/I71052956"],"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":"Article"},{"id":"pmh:oai:arXiv.org:1003.0292","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1003.0292","pdf_url":"https://arxiv.org/pdf/1003.0292","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":"pmh:oai:purehost.bath.ac.uk:publications/b53f40a3-6a42-42f0-bd0e-bccc5fb4ab16","is_oa":true,"landing_page_url":"https://researchportal.bath.ac.uk/en/publications/b53f40a3-6a42-42f0-bd0e-bccc5fb4ab16","pdf_url":"https://purehost.bath.ac.uk/ws/files/202116315/1003.0292v1.pdf","source":{"id":"https://openalex.org/S4377196294","display_name":"Pure (University of Bath)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I51601045","host_organization_name":"University of Bath","host_organization_lineage":["https://openalex.org/I51601045"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Lakkis, O & Pryer, T 2011, 'A finite element method for second order nonvariational elliptic problems', SIAM Journal on Scientific Computing, vol. 33, no. 2, pp. 786-801. https://doi.org/10.1137/100787672","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:alma.39UBZ_INST:11291748230001241","is_oa":false,"landing_page_url":"http://epubs.siam.org/doi/abs/10.1137/100787672","pdf_url":null,"source":{"id":"https://openalex.org/S4210197018","display_name":"View","issn_l":"2688-268X","issn":["2688-268X","2688-3988"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:kar.kent.ac.uk:31256","is_oa":false,"landing_page_url":"https://kar.kent.ac.uk/31256/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196264","display_name":"Kent Academic Repository (University of Kent)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20581793","host_organization_name":"University of Kent","host_organization_lineage":["https://openalex.org/I20581793"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:unibz.it:11291748230001241","is_oa":false,"landing_page_url":"https://bia.unibz.it/esploro/outputs/journalArticle/A-finite-element-method-for-second/991006483097201241","pdf_url":null,"source":{"id":"https://openalex.org/S4210197018","display_name":"View","issn_l":"2688-268X","issn":["2688-268X","2688-3988"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1003.0292","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1003.0292","pdf_url":"https://arxiv.org/pdf/1003.0292","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2038580008.pdf","grobid_xml":"https://content.openalex.org/works/W2038580008.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W2002707718","https://openalex.org/W2011600769","https://openalex.org/W2039914256","https://openalex.org/W2068875595","https://openalex.org/W2071415238","https://openalex.org/W2078897669","https://openalex.org/W2101577814","https://openalex.org/W2165512200","https://openalex.org/W2313087217"],"related_works":[],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,36,54],"numerical":[3],"method":[4,18,66],"to":[5,30,58],"approximate":[6],"the":[7,31,60],"solution":[8],"of":[9,20,35,49],"second":[10,37],"order":[11,38],"elliptic":[12,40],"problems":[13],"in":[14,80],"nonvariational":[15,32,81],"form.":[16,82],"The":[17,42,65],"is":[19,67],"Galerkin":[21],"type":[22],"using":[23],"conforming":[24],"finite":[25],"elements":[26],"and":[27,53,75],"applied":[28],"directly":[29],"(nondivergence)":[33],"form":[34],"linear":[39,62,74],"problem.":[41,64],"key":[43],"tools":[44],"are":[45],"an":[46],"appropriate":[47],"concept":[48],"\u201cfinite":[50],"element":[51],"Hessian\u201d":[52],"Schur":[55],"complement":[56],"approach":[57],"solving":[59],"resulting":[61],"algebra":[63],"illustrated":[68],"with":[69],"computational":[70],"experiments":[71],"on":[72],"three":[73],"one":[76],"quasi-linear":[77],"PDE,":[78],"all":[79]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2016-06-24T00:00:00"}