{"id":"https://openalex.org/W2956081464","doi":"https://doi.org/10.1137/18m121318x","title":"A Higher Degree Immersed Finite Element Method Based on a Cauchy Extension for Elliptic Interface Problems","display_name":"A Higher Degree Immersed Finite Element Method Based on a Cauchy Extension for Elliptic Interface Problems","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2956081464","doi":"https://doi.org/10.1137/18m121318x","mag":"2956081464"},"language":"en","primary_location":{"id":"doi:10.1137/18m121318x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m121318x","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":"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/A5003060391","display_name":"Ruchi Guo","orcid":"https://orcid.org/0000-0002-8558-1574"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ruchi Guo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5079719098","display_name":"Tao Lin","orcid":"https://orcid.org/0000-0002-7771-3936"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tao Lin","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":4.1108,"has_fulltext":false,"cited_by_count":47,"citation_normalized_percentile":{"value":0.95276225,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"57","issue":"4","first_page":"1545","last_page":"1573"},"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":0.9994999766349792,"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":0.9994999766349792,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9980000257492065,"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/mathematics","display_name":"Mathematics","score":0.7824403047561646},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.651577889919281},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.594033420085907},{"id":"https://openalex.org/keywords/discontinuity","display_name":"Discontinuity (linguistics)","score":0.5836761593818665},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.5570491552352905},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.5382897853851318},{"id":"https://openalex.org/keywords/interface","display_name":"Interface (matter)","score":0.5222431421279907},{"id":"https://openalex.org/keywords/degree-of-a-polynomial","display_name":"Degree of a polynomial","score":0.5011968612670898},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.4408491253852844},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4382503032684326},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39860212802886963},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3951708674430847},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.25117331743240356},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2004794180393219},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10550856590270996}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7824403047561646},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.651577889919281},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.594033420085907},{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.5836761593818665},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.5570491552352905},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.5382897853851318},{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.5222431421279907},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.5011968612670898},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.4408491253852844},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4382503032684326},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39860212802886963},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3951708674430847},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.25117331743240356},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2004794180393219},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10550856590270996},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C129307140","wikidata":"https://www.wikidata.org/wiki/Q6795880","display_name":"Maximum bubble pressure method","level":3,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","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/C157915830","wikidata":"https://www.wikidata.org/wiki/Q2928001","display_name":"Bubble","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/18m121318x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m121318x","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1514658588","https://openalex.org/W1572985915","https://openalex.org/W1979510989","https://openalex.org/W1988228958","https://openalex.org/W1993681020","https://openalex.org/W1997235068","https://openalex.org/W1997612340","https://openalex.org/W2012437014","https://openalex.org/W2014983931","https://openalex.org/W2016896593","https://openalex.org/W2029909883","https://openalex.org/W2030137526","https://openalex.org/W2040896717","https://openalex.org/W2042669113","https://openalex.org/W2043533888","https://openalex.org/W2050514923","https://openalex.org/W2052275102","https://openalex.org/W2058398001","https://openalex.org/W2065363406","https://openalex.org/W2076568557","https://openalex.org/W2092011174","https://openalex.org/W2141613219","https://openalex.org/W2144512254","https://openalex.org/W2157721313","https://openalex.org/W2168805210","https://openalex.org/W2192585930","https://openalex.org/W2196891435","https://openalex.org/W2400336179","https://openalex.org/W2559966930","https://openalex.org/W2770873983","https://openalex.org/W2963324830","https://openalex.org/W2963959289"],"related_works":["https://openalex.org/W1557607869","https://openalex.org/W2366350639","https://openalex.org/W2028455732","https://openalex.org/W4313703117","https://openalex.org/W2087496541","https://openalex.org/W2108615321","https://openalex.org/W1984758362","https://openalex.org/W2803854261","https://openalex.org/W2256082647","https://openalex.org/W2922694596"],"abstract_inverted_index":{"This":[0],"article":[1],"develops":[2],"and":[3,75,114,136],"analyzes":[4],"a":[5,45,97],"$p$th":[6,34],"degree":[7,35],"immersed":[8],"finite":[9],"element":[10,52],"(IFE)":[11],"method":[12,129],"for":[13],"solving":[14,44],"the":[15,23,27,55,61,70,76,82,92,105,110,126,134],"elliptic":[16],"interface":[17,51,56,73,77],"problems":[18],"with":[19],"meshes":[20],"independent":[21],"of":[22,64,72,99,109],"coefficient":[24],"discontinuity":[25],"in":[26,81,96,132],"involved":[28],"partial":[29],"differential":[30],"equations.":[31],"The":[32],"proposed":[33,83,93,127],"IFE":[36,65,84,94,112,128],"functions":[37,95],"are":[38,79,88,119],"macro":[39,100],"polynomials":[40],"constructed":[41],"by":[42],"weakly":[43],"Cauchy":[46],"problem":[47],"locally":[48],"on":[49,68],"each":[50],"according":[53],"to":[54,90,123],"jump":[57],"conditions.":[58],"To":[59],"alleviate":[60],"discontinuous":[62],"effects":[63],"functions,":[66],"penalties":[67],"both":[69,133],"edges":[71],"elements":[74],"itself":[78],"employed":[80],"scheme.":[85],"New":[86],"techniques":[87],"introduced":[89],"analyze":[91],"format":[98],"polynomials,":[101],"including":[102],"their":[103],"existence,":[104],"optimal":[106],"approximation":[107],"capabilities":[108],"resulting":[111],"spaces,":[113],"trace":[115],"inequalities.":[116],"These":[117],"results":[118],"then":[120],"further":[121],"applied":[122],"prove":[124],"that":[125],"converges":[130],"optimally":[131],"$L^2$":[135],"$H^1$":[137],"norms.":[138]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}