{"id":"https://openalex.org/W1987290411","doi":"https://doi.org/10.1080/00207160.2015.1005010","title":"Augmented immersed finite element methods for some elliptic partial differential equations","display_name":"Augmented immersed finite element methods for some elliptic partial differential equations","publication_year":2015,"publication_date":"2015-01-13","ids":{"openalex":"https://openalex.org/W1987290411","doi":"https://doi.org/10.1080/00207160.2015.1005010","mag":"1987290411"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2015.1005010","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1005010","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5005597390","display_name":"Haifeng Ji","orcid":"https://orcid.org/0000-0001-6812-1907"},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haifeng Ji","raw_affiliation_strings":["School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing210023, China","School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing210023, China#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing210023, China","institution_ids":["https://openalex.org/I152031979"]},{"raw_affiliation_string":"School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing210023, China#TAB#","institution_ids":["https://openalex.org/I152031979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034304672","display_name":"Jinru Chen","orcid":"https://orcid.org/0000-0002-2761-2926"},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jinru Chen","raw_affiliation_strings":["School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing210023, China","School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing210023, China#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing210023, China","institution_ids":["https://openalex.org/I152031979"]},{"raw_affiliation_string":"School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing210023, China#TAB#","institution_ids":["https://openalex.org/I152031979"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101930655","display_name":"Zhilin Li","orcid":"https://orcid.org/0000-0002-1636-5376"},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]},{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Zhilin Li","raw_affiliation_strings":["School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing210023, China;Department of Mathematics, North Carolina State University, Raleigh, NC27695, USA","Department of Mathematics, North Carolina State University, Raleigh, NC27695, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing210023, China;Department of Mathematics, North Carolina State University, Raleigh, NC27695, USA","institution_ids":["https://openalex.org/I152031979"]},{"raw_affiliation_string":"Department of Mathematics, North Carolina State University, Raleigh, NC27695, USA#TAB#","institution_ids":["https://openalex.org/I137902535"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5034304672"],"corresponding_institution_ids":["https://openalex.org/I152031979"],"apc_list":null,"apc_paid":null,"fwci":1.2995,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.78523074,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"93","issue":"3","first_page":"540","last_page":"558"},"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":0.9995999932289124,"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":0.9995999932289124,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9994000196456909,"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":0.9987999796867371,"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":0.8006258010864258},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6514090299606323},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6226878762245178},{"id":"https://openalex.org/keywords/poissons-equation","display_name":"Poisson's equation","score":0.5524526834487915},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5324923396110535},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.5084149241447449},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5019786357879639},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4084486663341522}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8006258010864258},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6514090299606323},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6226878762245178},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.5524526834487915},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5324923396110535},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.5084149241447449},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5019786357879639},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4084486663341522},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2015.1005010","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1005010","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W285197588","https://openalex.org/W309443866","https://openalex.org/W592368443","https://openalex.org/W1480560153","https://openalex.org/W1525818589","https://openalex.org/W1965130545","https://openalex.org/W1981891092","https://openalex.org/W1993371992","https://openalex.org/W1997235068","https://openalex.org/W1997612340","https://openalex.org/W2006206329","https://openalex.org/W2014475794","https://openalex.org/W2016896593","https://openalex.org/W2030137526","https://openalex.org/W2031746041","https://openalex.org/W2040896717","https://openalex.org/W2042669113","https://openalex.org/W2058398001","https://openalex.org/W2066215158","https://openalex.org/W2073237947","https://openalex.org/W2079823607","https://openalex.org/W2085426491","https://openalex.org/W2092445105","https://openalex.org/W2095548561","https://openalex.org/W2099193593","https://openalex.org/W2116434326","https://openalex.org/W2119611099","https://openalex.org/W2123584617","https://openalex.org/W2135631181","https://openalex.org/W2140153041","https://openalex.org/W2144512254","https://openalex.org/W2155704971","https://openalex.org/W2528125524","https://openalex.org/W2599621596","https://openalex.org/W3140864197","https://openalex.org/W3151858025","https://openalex.org/W4247257561","https://openalex.org/W4254163830"],"related_works":["https://openalex.org/W2351666715","https://openalex.org/W2757332726","https://openalex.org/W1967543778","https://openalex.org/W2382902960","https://openalex.org/W2385263368","https://openalex.org/W2055836843","https://openalex.org/W2369384937","https://openalex.org/W2347422947","https://openalex.org/W2793265400","https://openalex.org/W642325214"],"abstract_inverted_index":{"Augmented":[0],"immersed":[1],"finite":[2],"element":[3],"methods":[4],"are":[5,20,138],"proposed":[6],"to":[7,42,78,102,117],"solve":[8,79,118],"elliptic":[9],"interface":[10,40],"problems":[11],"with":[12,46],"non-homogeneous":[13,17],"jump":[14,18,49,57,68,106],"conditions.":[15],"The":[16,72,83],"conditions":[19],"treated":[21],"as":[22],"source":[23],"terms":[24],"using":[25,93],"the":[26,31,38,47,51,65,80,104,112,130,135,142],"singularity":[27],"removal":[28],"technique.":[29],"For":[30],"piecewise":[32],"constant":[33],"coefficient":[34],"case,":[35],"we":[36],"transform":[37],"original":[39,66],"problem":[41],"a":[43,90,94,109],"Poisson":[44,91,96,119],"equation":[45,92],"same":[48],"in":[50,141],"solution,":[52],"but":[53,133],"an":[54,99],"unknown":[55],"flux":[56,67,105],"(augmented":[58],"variable)":[59],"which":[60],"is":[61,70,76],"chosen":[62],"such":[63],"that":[64,127],"condition":[69],"satisfied.":[71],"GMRES":[73],"iterative":[74],"method":[75,113],"used":[77],"augmented":[81],"variable.":[82],"core":[84],"of":[85],"each":[86],"iteration":[87],"involves":[88],"solving":[89],"fast":[95],"solver":[97],"and":[98],"interpolation":[100],"scheme":[101],"interpolate":[103],"condition.":[107],"With":[108],"little":[110],"modification,":[111],"can":[114],"be":[115],"applied":[116],"equations":[120],"on":[121],"irregular":[122],"domains.":[123],"Numerical":[124],"experiments":[125],"show":[126],"not":[128],"only":[129],"computed":[131],"solution":[132],"also":[134],"normal":[136],"derivative":[137],"second-order":[139],"accurate":[140],"L\u221e":[143],"norm.":[144]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}