{"id":"https://openalex.org/W2064561253","doi":"https://doi.org/10.1137/090752407","title":"A Novel Least-Squares Finite Element Method Enriched with Residual-Free Bubbles for Solving Convection-Dominated Problems","display_name":"A Novel Least-Squares Finite Element Method Enriched with Residual-Free Bubbles for Solving Convection-Dominated Problems","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2064561253","doi":"https://doi.org/10.1137/090752407","mag":"2064561253"},"language":"en","primary_location":{"id":"doi:10.1137/090752407","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090752407","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/A5008764613","display_name":"Po\u2010Wen Hsieh","orcid":"https://orcid.org/0000-0001-8235-7393"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Po-Wen Hsieh","raw_affiliation_strings":["952401001@cc.ncu.edu.tw and syyang@math.ncu.edu.tw#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"952401001@cc.ncu.edu.tw and syyang@math.ncu.edu.tw#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060279477","display_name":"Suh\u2010Yuh Yang","orcid":"https://orcid.org/0000-0001-9427-0981"},"institutions":[{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Suh-Yuh Yang","raw_affiliation_strings":["Department of Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics","institution_ids":["https://openalex.org/I530967"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0052,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.77730351,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"32","issue":"4","first_page":"2047","last_page":"2073"},"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":0.9994000196456909,"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":0.9994000196456909,"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":0.7555092573165894},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5956372618675232},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5943252444267273},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5622774362564087},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.5542819499969482},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5287083387374878},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5190213918685913},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.50344318151474},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.48139145970344543},{"id":"https://openalex.org/keywords/nabla-symbol","display_name":"Nabla symbol","score":0.4661743640899658},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.4553925395011902},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.421498566865921},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.41907182335853577},{"id":"https://openalex.org/keywords/bubble","display_name":"Bubble","score":0.41887474060058594},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2715074121952057},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.18292418122291565},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1775149405002594},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.14321425557136536},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13200294971466064},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.11813586950302124}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7555092573165894},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5956372618675232},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5943252444267273},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5622774362564087},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.5542819499969482},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5287083387374878},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5190213918685913},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.50344318151474},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.48139145970344543},{"id":"https://openalex.org/C54207081","wikidata":"https://www.wikidata.org/wiki/Q937750","display_name":"Nabla symbol","level":3,"score":0.4661743640899658},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.4553925395011902},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.421498566865921},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.41907182335853577},{"id":"https://openalex.org/C157915830","wikidata":"https://www.wikidata.org/wiki/Q2928001","display_name":"Bubble","level":2,"score":0.41887474060058594},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2715074121952057},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.18292418122291565},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1775149405002594},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.14321425557136536},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13200294971466064},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.11813586950302124},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/090752407","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090752407","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":[],"funders":[{"id":"https://openalex.org/F4320309398","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W316634611","https://openalex.org/W1492326914","https://openalex.org/W1555557982","https://openalex.org/W1583880678","https://openalex.org/W1674659126","https://openalex.org/W1852082788","https://openalex.org/W1974006019","https://openalex.org/W1976509668","https://openalex.org/W1979560958","https://openalex.org/W1980986560","https://openalex.org/W2009852560","https://openalex.org/W2010468148","https://openalex.org/W2011185352","https://openalex.org/W2028587964","https://openalex.org/W2029918260","https://openalex.org/W2034081303","https://openalex.org/W2040009281","https://openalex.org/W2046002450","https://openalex.org/W2060170348","https://openalex.org/W2065438814","https://openalex.org/W2065920748","https://openalex.org/W2073897969","https://openalex.org/W2074330728","https://openalex.org/W2076160755","https://openalex.org/W2078892983","https://openalex.org/W2079114130","https://openalex.org/W2081177856","https://openalex.org/W2092486420","https://openalex.org/W2099656682","https://openalex.org/W2126715817","https://openalex.org/W2132292023","https://openalex.org/W2148598908","https://openalex.org/W2155879256","https://openalex.org/W2161259477","https://openalex.org/W2289366489","https://openalex.org/W2489432230","https://openalex.org/W3149667697","https://openalex.org/W4230108662","https://openalex.org/W4250155727"],"related_works":["https://openalex.org/W2229925025","https://openalex.org/W1539596337","https://openalex.org/W33469805","https://openalex.org/W1855007440","https://openalex.org/W2788247819","https://openalex.org/W2914699178","https://openalex.org/W2072209417","https://openalex.org/W2010923956","https://openalex.org/W2096438264","https://openalex.org/W2090448379"],"abstract_inverted_index":{"In":[0,231],"this":[1,102,177],"paper":[2],"we":[3,19],"devise":[4],"a":[5,21,26,106,193,224,238,242],"novel":[6],"least-squares":[7,104],"finite":[8],"element":[9,98],"method":[10,108,152],"(LSFEM)":[11],"for":[12,51,192,250],"solving":[13,251],"scalar":[14],"convection-dominated":[15,252],"convection-diffusion":[16,23,78],"problems.":[17,253],"First,":[18],"convert":[20],"second-order":[22,77],"problem":[24],"into":[25],"first-order":[27,62],"system":[28,137],"formulation":[29],"by":[30],"introducing":[31],"the":[32,61,74,81,88,91,97,116,126,129,134,146,149,164,167,186,197,206,212,215,220,234,247],"gradient":[33],"$\\mathbf{p}:=-\\kappa\\nabla":[34],"u$":[35],"as":[36,133],"an":[37],"additional":[38],"variable.":[39],"The":[40,65,171],"LSFEM":[41,122,179,199,222,236,249],"using":[42],"continuous":[43],"piecewise":[44],"linear":[45,92,136],"elements":[46],"enriched":[47,121,169,178,198,235],"with":[48,183,241],"residual-free":[49,66,117,150],"bubbles":[50],"both":[52],"variables":[53],"u":[54],"and":[55,94,140,173],"$\\mathbf{p}$":[56],"is":[57,112,200],"applied":[58],"to":[59,71,87,114,162,204],"solve":[60],"mixed":[63],"problem.":[64],"bubble":[67,118,151],"functions":[68],"are":[69,160,180],"assumed":[70],"strongly":[72],"satisfy":[73],"associated":[75],"homogeneous":[76],"equations":[79],"in":[80,211],"interior":[82],"of":[83,90,109,128,148,166,176,185,208],"each":[84],"element,":[85],"up":[86],"contribution":[89],"part,":[93],"vanish":[95],"on":[96],"boundary.":[99],"To":[100],"implement":[101],"two-level":[103],"approach,":[105],"stabilized":[107],"Galerkin/least-squares":[110],"type":[111],"used":[113],"approximate":[115],"functions.":[119],"This":[120],"not":[123],"only":[124],"inherits":[125],"advantages":[127],"primitive":[130,187,216,221,248],"LSFEM,":[131,217],"such":[132],"resulting":[135],"being":[138],"symmetric":[139],"positive":[141],"definite,":[142],"but":[143],"also":[144,181],"exhibits":[145],"characteristics":[147],"without":[153],"involving":[154],"stability":[155],"parameters.":[156],"Several":[157],"numerical":[158],"experiments":[159],"given":[161],"demonstrate":[163],"effectiveness":[165],"proposed":[168],"LSFEM.":[170,188],"accuracy":[172],"computational":[174,244],"cost":[175],"compared":[182],"those":[184],"We":[189],"find":[190],"that":[191],"small":[194],"diffusivity":[195],"$\\kappa$,":[196],"much":[201],"better":[202],"able":[203],"capture":[205],"nature":[207],"layer":[209],"structure":[210],"solution":[213],"than":[214],"even":[218],"if":[219],"uses":[223],"very":[225],"fine":[226],"mesh":[227],"or":[228],"higher-order":[229],"elements.":[230],"other":[232],"words,":[233],"provides":[237],"significant":[239],"improvement,":[240],"lower":[243],"cost,":[245],"over":[246]},"counts_by_year":[{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}