{"id":"https://openalex.org/W1976375362","doi":"https://doi.org/10.1137/s0036142999361517","title":"Conservative<i>P</i>1 Conforming and Nonconforming Galerkin FEMs: Effective Flux Evaluation via a Nonmixed Method Approach","display_name":"Conservative<i>P</i>1 Conforming and Nonconforming Galerkin FEMs: Effective Flux Evaluation via a Nonmixed Method Approach","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1976375362","doi":"https://doi.org/10.1137/s0036142999361517","mag":"1976375362"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142999361517","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999361517","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/A5027876548","display_name":"So\u2010Hsiang Chou","orcid":"https://orcid.org/0000-0001-8371-1219"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"So-Hsiang Chou","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5070094203","display_name":"Shengrong Tang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shengrong Tang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027876548"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.753,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.92030885,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"38","issue":"2","first_page":"660","last_page":"680"},"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":0.9997000098228455,"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":0.9997000098228455,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9980999827384949,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9961000084877014,"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":0.8496907949447632},{"id":"https://openalex.org/keywords/nabla-symbol","display_name":"Nabla symbol","score":0.7571226358413696},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7013600468635559},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6754884719848633},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5314912796020508},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.5017549991607666},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.48496055603027344},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.43932706117630005},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4016697108745575},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.39155271649360657},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21664533019065857},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12472736835479736}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8496907949447632},{"id":"https://openalex.org/C54207081","wikidata":"https://www.wikidata.org/wiki/Q937750","display_name":"Nabla symbol","level":3,"score":0.7571226358413696},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7013600468635559},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6754884719848633},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5314912796020508},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.5017549991607666},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.48496055603027344},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.43932706117630005},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4016697108745575},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.39155271649360657},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21664533019065857},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12472736835479736},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142999361517","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999361517","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":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.7200000286102295}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1492326914","https://openalex.org/W1965791168","https://openalex.org/W1967953674","https://openalex.org/W1976718653","https://openalex.org/W2015391903","https://openalex.org/W2035728289","https://openalex.org/W2054833806","https://openalex.org/W2055947420","https://openalex.org/W2069697314","https://openalex.org/W2480154215","https://openalex.org/W2491027544","https://openalex.org/W2516518242","https://openalex.org/W2592623476","https://openalex.org/W4285719527","https://openalex.org/W4292166829"],"related_works":["https://openalex.org/W2792440356","https://openalex.org/W3112745479","https://openalex.org/W4378474062","https://openalex.org/W2012174435","https://openalex.org/W2523130954","https://openalex.org/W2927373829","https://openalex.org/W1973083629","https://openalex.org/W2383924526","https://openalex.org/W4234704706","https://openalex.org/W4205474276"],"abstract_inverted_index":{"Given":[0],"a":[1,56,87,144,152],"P1":[2],"conforming":[3],"or":[4,76,108],"nonconforming":[5],"Galerkin":[6],"finite":[7,64,109,155],"element":[8,100,107],"method":[9,93,123,133,142],"(GFEM)":[10],"solution":[11,17],"ph,":[12],"which":[13],"approximates":[14],"the":[15,20,43,48,71,77,99,121,125,128,131,164,172,178,185,194],"exact":[16,49],"p":[18,27,30],"of":[19,84,103,127,181],"diffusion-reaction":[21],"equation":[22],"$":[23,33],"-\\nabla\\cdot":[24],"{\\mathcal":[25],"K}\\nabla":[26,53],"+":[28],"\\alpha":[29],"=":[31],"f":[32],"with":[34],"full":[35],"tensor":[36],"variable":[37],"coefficient":[38],"${\\mathcal":[39],"K}$,":[40],"we":[41,139],"evaluate":[42],"approximate":[44],"flux":[45,50,67,179],"uh":[46],"to":[47,151,192],"${\\bf":[51],"u}=-{\\mathcal":[52],"p$":[54],"by":[55],"simple":[57],"but":[58,112,134],"physically":[59],"intuitive":[60],"formula":[61,88],"over":[62],"each":[63],"element.":[65],"The":[66,159,175],"is":[68,89,180],"sought":[69],"in":[70,177,184],"continuous":[72],"(in":[73],"normal":[74],"component)":[75],"discontinuous":[78],"Raviart--Thomas":[79],"space.":[80],"A":[81],"systematic":[82],"way":[83],"deriving":[85],"such":[86],"introduced.":[90],"This":[91],"direct":[92],"retains":[94,124],"local":[95],"conservation":[96],"property":[97],"at":[98],"level,":[101],"typical":[102],"mixed":[104,132,154,173],"methods":[105],"(finite":[106],"volume":[110,156],"type),":[111],"avoids":[113],"solving":[114],"an":[115],"indefinite":[116],"linear":[117],"system.":[118],"In":[119],"short,":[120],"present":[122],"best":[126],"GFEM":[129,146],"and":[130,147],"without":[135],"their":[136],"shortcomings.":[137],"Thus":[138],"view":[140],"our":[141],"as":[143],"conservative":[145],"demonstrate":[148],"its":[149],"equivalence":[150,160],"certain":[153],"box":[157],"method.":[158],"theorems":[161],"explain":[162],"how":[163],"pressure":[165],"can":[166],"decouple":[167],"basically":[168],"cost":[169],"free":[170],"from":[171],"formulation.":[174],"accuracy":[176],"first":[182],"order":[183],"$H(\\dive;\\Omega)$":[186],"norm.":[187],"Numerical":[188],"results":[189],"are":[190],"provided":[191],"support":[193],"theory.":[195]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
