{"id":"https://openalex.org/W2075501190","doi":"https://doi.org/10.1090/s0025-5718-06-01950-8","title":"A locally divergence-free nonconforming finite element method for the time-harmonic Maxwell equations","display_name":"A locally divergence-free nonconforming finite element method for the time-harmonic Maxwell equations","publication_year":2006,"publication_date":"2006-12-27","ids":{"openalex":"https://openalex.org/W2075501190","doi":"https://doi.org/10.1090/s0025-5718-06-01950-8","mag":"2075501190"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-06-01950-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01950-8","pdf_url":"https://www.ams.org/mcom/2007-76-258/S0025-5718-06-01950-8/S0025-5718-06-01950-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2007-76-258/S0025-5718-06-01950-8/S0025-5718-06-01950-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061146602","display_name":"Susanne C. Brenner","orcid":"https://orcid.org/0000-0001-8330-5667"},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]},{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Susanne C. Brenner","raw_affiliation_strings":["Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803","Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803","institution_ids":["https://openalex.org/I121820613"]},{"raw_affiliation_string":"Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208","institution_ids":["https://openalex.org/I155781252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101926587","display_name":"Fengyan Li","orcid":"https://orcid.org/0000-0002-2386-7702"},"institutions":[{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]},{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fengyan Li","raw_affiliation_strings":["Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180","Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180","institution_ids":["https://openalex.org/I165799507"]},{"raw_affiliation_string":"Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208","institution_ids":["https://openalex.org/I155781252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5106083270","display_name":"Li-Yeng Sung","orcid":null},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]},{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Li-yeng Sung","raw_affiliation_strings":["Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803","Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803","institution_ids":["https://openalex.org/I121820613"]},{"raw_affiliation_string":"Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208","institution_ids":["https://openalex.org/I155781252"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.1696,"has_fulltext":true,"cited_by_count":66,"citation_normalized_percentile":{"value":0.93752399,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"76","issue":"258","first_page":"573","last_page":"595"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"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":0.9993000030517578,"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":0.86778324842453},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7559319734573364},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6628111600875854},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.6058220267295837},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6033720970153809},{"id":"https://openalex.org/keywords/maxwells-equations","display_name":"Maxwell's equations","score":0.5713324546813965},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5626412034034729},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.4953130781650543},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.44069960713386536},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3972207307815552},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12721753120422363},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09299823641777039}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.86778324842453},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7559319734573364},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6628111600875854},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.6058220267295837},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6033720970153809},{"id":"https://openalex.org/C59282198","wikidata":"https://www.wikidata.org/wiki/Q51501","display_name":"Maxwell's equations","level":2,"score":0.5713324546813965},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5626412034034729},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.4953130781650543},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.44069960713386536},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3972207307815552},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12721753120422363},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09299823641777039},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-06-01950-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01950-8","pdf_url":"https://www.ams.org/mcom/2007-76-258/S0025-5718-06-01950-8/S0025-5718-06-01950-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:digitalcommons.lsu.edu:mathematics_pubs-1171","is_oa":false,"landing_page_url":"https://digitalcommons.lsu.edu/mathematics_pubs/172","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"},{"id":"pmh:oai:repository.lsu.edu:mathematics_pubs-1171","is_oa":false,"landing_page_url":"https://repository.lsu.edu/mathematics_pubs/172","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-06-01950-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01950-8","pdf_url":"https://www.ams.org/mcom/2007-76-258/S0025-5718-06-01950-8/S0025-5718-06-01950-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.6499999761581421,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2075501190.pdf","grobid_xml":"https://content.openalex.org/works/W2075501190.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W86985056","https://openalex.org/W591292934","https://openalex.org/W618110921","https://openalex.org/W1492326914","https://openalex.org/W1582734821","https://openalex.org/W1586623601","https://openalex.org/W1674659126","https://openalex.org/W1994841670","https://openalex.org/W2000554621","https://openalex.org/W2041523977","https://openalex.org/W2067527388","https://openalex.org/W2068798260","https://openalex.org/W2071928229","https://openalex.org/W2077070913","https://openalex.org/W2103349556","https://openalex.org/W2117418968","https://openalex.org/W2592623476","https://openalex.org/W3100291325","https://openalex.org/W4205561485","https://openalex.org/W4232597038","https://openalex.org/W4241837011","https://openalex.org/W4250220742","https://openalex.org/W4252104256","https://openalex.org/W4299302210"],"related_works":["https://openalex.org/W1557607869","https://openalex.org/W2366350639","https://openalex.org/W2028455732","https://openalex.org/W4313703117","https://openalex.org/W2006251942","https://openalex.org/W2085564391","https://openalex.org/W2087496541","https://openalex.org/W2108615321","https://openalex.org/W1984758362","https://openalex.org/W2484549579"],"abstract_inverted_index":{"A":[0],"new":[1],"numerical":[2,82],"method":[3],"for":[4],"computing":[5],"the":[6,10,13,30,44,47,64,68],"divergence-free":[7,32],"part":[8],"of":[9,12,46],"solution":[11],"time-harmonic":[14],"Maxwell":[15],"equations":[16],"is":[17,23],"studied":[18],"in":[19,62],"this":[20],"paper.":[21],"It":[22],"based":[24],"on":[25,73],"a":[26,40],"discretization":[27],"that":[28],"uses":[29],"locally":[31],"Crouzeix-Raviart":[33],"nonconforming":[34],"$P_1$":[35],"vector":[36,48],"fields":[37,49],"and":[38,67],"includes":[39],"consistency":[41],"term":[42],"involving":[43],"jumps":[45],"across":[50],"element":[51],"boundaries.":[52],"Optimal":[53],"convergence":[54],"rates":[55],"(up":[56],"to":[57],"an":[58],"arbitrary":[59],"positive":[60],"$\\epsilon$)":[61],"both":[63],"energy":[65],"norm":[66,70],"$L_2$":[69],"are":[71,79],"established":[72],"graded":[74],"meshes.":[75],"The":[76],"theoretical":[77],"results":[78],"confirmed":[80],"by":[81],"experiments.":[83]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":11}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}