{"id":"https://openalex.org/W2785048882","doi":"https://doi.org/10.1137/16m1078082","title":"A Mixed $H^1$-Conforming Finite Element Method for Solving Maxwell's Equations with Non-$H^1$ Solution","display_name":"A Mixed $H^1$-Conforming Finite Element Method for Solving Maxwell's Equations with Non-$H^1$ Solution","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2785048882","doi":"https://doi.org/10.1137/16m1078082","mag":"2785048882"},"language":"en","primary_location":{"id":"doi:10.1137/16m1078082","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1078082","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":["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/A5111632843","display_name":"Huo-Yuan Duan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huo-Yuan Duan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109412865","display_name":"Roger C. E. Tan","orcid":"https://orcid.org/0009-0009-3531-2294"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Roger C. E. Tan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060279477","display_name":"Suh\u2010Yuh Yang","orcid":"https://orcid.org/0000-0001-9427-0981"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Suh-Yuh Yang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5111632844","display_name":"Cheng-Shu You","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cheng-Shu You","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":1.6026,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.80286311,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"40","issue":"1","first_page":"A224","last_page":"A250"},"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":0.9998999834060669,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9998000264167786,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7770450115203857},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7489866614341736},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.7078922390937805},{"id":"https://openalex.org/keywords/maxwells-equations","display_name":"Maxwell's equations","score":0.6739214062690735},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5485225915908813},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.5368457436561584},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.5128657817840576},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.48012518882751465},{"id":"https://openalex.org/keywords/extended-finite-element-method","display_name":"Extended finite element method","score":0.4393000602722168},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4314176142215729},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4256264567375183},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4145551025867462},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.16054034233093262},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12172368168830872}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7770450115203857},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7489866614341736},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.7078922390937805},{"id":"https://openalex.org/C59282198","wikidata":"https://www.wikidata.org/wiki/Q51501","display_name":"Maxwell's equations","level":2,"score":0.6739214062690735},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5485225915908813},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.5368457436561584},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.5128657817840576},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.48012518882751465},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.4393000602722168},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4314176142215729},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4256264567375183},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4145551025867462},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.16054034233093262},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12172368168830872},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1078082","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1078082","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2599784737","display_name":null,"funder_award_id":"MOST 106-2811-M-008-004","funder_id":"https://openalex.org/F4320322795","funder_display_name":"Ministry of Science and Technology, Taiwan"},{"id":"https://openalex.org/G2863854969","display_name":null,"funder_award_id":"11171168","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4006891518","display_name":null,"funder_award_id":"11661161017","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5070314477","display_name":null,"funder_award_id":"MOST 103-2115-M-008-009-MY3","funder_id":"https://openalex.org/F4320322795","funder_display_name":"Ministry of Science and Technology, Taiwan"},{"id":"https://openalex.org/G5152986006","display_name":null,"funder_award_id":"91430106","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7735700187","display_name":null,"funder_award_id":"11571266","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322795","display_name":"Ministry of Science and Technology, Taiwan","ror":"https://ror.org/02kv4zf79"},{"id":"https://openalex.org/F4320324116","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W6095528","https://openalex.org/W194323848","https://openalex.org/W581329602","https://openalex.org/W1492326914","https://openalex.org/W1527335220","https://openalex.org/W1582734821","https://openalex.org/W1674659126","https://openalex.org/W1970198065","https://openalex.org/W1970402902","https://openalex.org/W1972904830","https://openalex.org/W1973835324","https://openalex.org/W1983989325","https://openalex.org/W1984701620","https://openalex.org/W1989748191","https://openalex.org/W1995414190","https://openalex.org/W2000554621","https://openalex.org/W2005436751","https://openalex.org/W2005562482","https://openalex.org/W2006085156","https://openalex.org/W2011724566","https://openalex.org/W2013434737","https://openalex.org/W2014753166","https://openalex.org/W2032997846","https://openalex.org/W2041523977","https://openalex.org/W2050496851","https://openalex.org/W2056431505","https://openalex.org/W2060214090","https://openalex.org/W2065196236","https://openalex.org/W2067392615","https://openalex.org/W2068798260","https://openalex.org/W2071704402","https://openalex.org/W2081729435","https://openalex.org/W2088014397","https://openalex.org/W2089167308","https://openalex.org/W2090343972","https://openalex.org/W2096578056","https://openalex.org/W2100188483","https://openalex.org/W2125409504","https://openalex.org/W2128663529","https://openalex.org/W2139094627","https://openalex.org/W2140888248","https://openalex.org/W2143783905","https://openalex.org/W2157129549","https://openalex.org/W2160005782","https://openalex.org/W2163440807","https://openalex.org/W2168762452","https://openalex.org/W2224192171","https://openalex.org/W2305890161","https://openalex.org/W2489432230","https://openalex.org/W3149667697","https://openalex.org/W4243893532","https://openalex.org/W4246282634","https://openalex.org/W4299302210"],"related_works":["https://openalex.org/W1973265389","https://openalex.org/W2051305457","https://openalex.org/W150665603","https://openalex.org/W4299609681","https://openalex.org/W1977314144","https://openalex.org/W4281485387","https://openalex.org/W2387622977","https://openalex.org/W430044182","https://openalex.org/W1990305831","https://openalex.org/W2785048882"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"propose":[4],"and":[5,22,47,70,102,121,125,128,147],"analyze":[6],"a":[7,65,108],"mixed":[8,94,160],"$H^1$-conforming":[9,111,161],"finite":[10,112,162],"element":[11,163],"method":[12,78],"for":[13,31,118,136],"solving":[14],"Maxwell's":[15,61],"equations":[16,62],"in":[17,81],"terms":[18],"of":[19,60,100,110,157],"electric":[20,119],"field":[21,120],"Lagrange":[23],"multiplier,":[24],"where":[25],"the":[26,32,39,42,58,82,93,115,145,154,158],"multiplier":[27,122],"is":[28,45,79,105,123],"introduced":[29],"accounting":[30],"divergence":[33],"constraint.":[34],"We":[35],"mainly":[36],"focus":[37],"on":[38,144],"case":[40],"that":[41],"physical":[43],"domain":[44],"nonconvex":[46],"its":[48,126],"boundary":[49],"includes":[50],"reentrant":[51],"corners":[52],"or":[53],"edges,":[54],"which":[55],"may":[56],"lead":[57],"solution":[59],"to":[63,92,152],"be":[64],"non-$H^1$":[66],"very":[67],"weak":[68],"function":[69],"thus":[71],"cause":[72],"many":[73],"numerical":[74],"difficulties.":[75],"The":[76],"proposed":[77,159],"formulated":[80],"stabilized":[83],"form":[84],"by":[85],"adding":[86],"an":[87],"additional":[88],"mesh-dependent":[89],"stabilization":[90],"term":[91],"variational":[95],"formulation.":[96],"A":[97],"general":[98],"framework":[99],"stability":[101,127],"error":[103,129],"analysis":[104],"established.":[106],"Specifically,":[107],"pair":[109],"elements,":[113,117],"namely,":[114],"$CP_2$-$P_1$":[116],"studied,":[124],"bounds":[130],"are":[131,150],"also":[132],"derived.":[133],"Numerical":[134],"experiments":[135],"source":[137],"problems":[138,143],"as":[139,141],"well":[140],"eigenvalue":[142],"$L$-shaped":[146],"cracked":[148],"domains":[149],"presented":[151],"illustrate":[153],"high":[155],"performance":[156],"method.":[164]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}