{"id":"https://openalex.org/W2001883934","doi":"https://doi.org/10.1137/090753735","title":"Fully Discrete Finite Element Approximations of a Polymer Gel Model","display_name":"Fully Discrete Finite Element Approximations of a Polymer Gel Model","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2001883934","doi":"https://doi.org/10.1137/090753735","mag":"2001883934"},"language":"en","primary_location":{"id":"doi:10.1137/090753735","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090753735","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/A5011365911","display_name":"Xiaobing Feng","orcid":"https://orcid.org/0000-0002-9191-9092"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Xiaobing Feng","raw_affiliation_strings":["xfeng@math.utk.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"xfeng@math.utk.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100457891","display_name":"Yinnian He","orcid":"https://orcid.org/0000-0003-3402-8493"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yinnian He","raw_affiliation_strings":["heyn@mail.xjtu.edu.cn#TAB#"],"affiliations":[{"raw_affiliation_string":"heyn@mail.xjtu.edu.cn#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5011365911"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3432,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.62555383,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"48","issue":"6","first_page":"2186","last_page":"2217"},"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":0.9890999794006348,"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":0.9890999794006348,"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/T11366","display_name":"Elasticity and Material Modeling","score":0.9855999946594238,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9829999804496765,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multiphysics","display_name":"Multiphysics","score":0.8285801410675049},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7584562301635742},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.7086695432662964},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5437619686126709},{"id":"https://openalex.org/keywords/stokes-flow","display_name":"Stokes flow","score":0.49794697761535645},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.4923657178878784},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48343953490257263},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4536839723587036},{"id":"https://openalex.org/keywords/displacement-field","display_name":"Displacement field","score":0.4380573034286499},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4361782670021057},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.42911863327026367},{"id":"https://openalex.org/keywords/displacement","display_name":"Displacement (psychology)","score":0.4138273596763611},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.410469651222229},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3740656077861786},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3591229021549225},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1572064459323883},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.1450972557067871},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1440519094467163}],"concepts":[{"id":"https://openalex.org/C46435376","wikidata":"https://www.wikidata.org/wiki/Q1829750","display_name":"Multiphysics","level":3,"score":0.8285801410675049},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7584562301635742},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7086695432662964},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5437619686126709},{"id":"https://openalex.org/C19191322","wikidata":"https://www.wikidata.org/wiki/Q674202","display_name":"Stokes flow","level":3,"score":0.49794697761535645},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.4923657178878784},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48343953490257263},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4536839723587036},{"id":"https://openalex.org/C29660869","wikidata":"https://www.wikidata.org/wiki/Q5282615","display_name":"Displacement field","level":3,"score":0.4380573034286499},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4361782670021057},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.42911863327026367},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.4138273596763611},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.410469651222229},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3740656077861786},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3591229021549225},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1572064459323883},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.1450972557067871},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1440519094467163},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","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/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/090753735","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090753735","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/7","display_name":"Affordable and clean energy","score":0.49000000953674316}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W2000120977","https://openalex.org/W2003034707","https://openalex.org/W2016064602","https://openalex.org/W2032720610","https://openalex.org/W2060471433","https://openalex.org/W2067392615","https://openalex.org/W2082969232","https://openalex.org/W2149890054","https://openalex.org/W4241126398"],"related_works":["https://openalex.org/W2084426624","https://openalex.org/W3026055904","https://openalex.org/W2792869497","https://openalex.org/W4312133600","https://openalex.org/W2567205727","https://openalex.org/W2361803029","https://openalex.org/W2548694948","https://openalex.org/W2010566957","https://openalex.org/W2304501688","https://openalex.org/W1970503344"],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"and":[3,77,117,151,229,252,284,301],"analyzes":[4],"some":[5,257],"fully":[6,253,285],"discrete":[7,254,258,286],"(multiphysics)":[8],"finite":[9,209,217],"element":[10,210,218],"methods":[11,255],"for":[12,65,84,113,124,147,169,281],"a":[13,34,43,62,81,85,97,120,166,244],"displacement-pressure":[14],"model":[15],"which":[16,46,60,261],"describes":[17],"swelling":[18],"dynamics":[19],"of":[20,36,59,74,91,234,297],"polymer":[21,200],"gels":[22],"under":[23,243],"mechanical":[24],"constraints.":[25],"By":[26],"introducing":[27],"an":[28,223],"\u201celastic":[29],"pressure\u201d":[30],"we":[31],"first":[32,139],"present":[33,226],"reformulation":[35],"the":[37,48,66,71,75,78,89,92,110,114,125,138,148,152,155,161,170,199,204,206,214,227,232,235,248,263,269,295,298],"original":[38],"model.":[39,202],"We":[40],"then":[41],"propose":[42],"time-stepping":[44,174],"scheme":[45,175],"decouples":[47],"PDE":[49,149,270],"system":[50],"at":[51],"each":[52],"time":[53],"step":[54],"into":[55],"two":[56],"subproblems,":[57],"one":[58,177],"is":[61,80,102,141,158,240],"Stokes-like":[63,115,162],"problem":[64,83,116,163],"displacement":[67],"vector":[68],"field":[69,87],"(of":[70,88],"solid":[72],"network":[73],"gel)":[76],"other":[79],"diffusion":[82,126,171,191],"\u201cpseudopressure\u201d":[86],"solvent":[90],"gel).":[93],"To":[94],"make":[95],"such":[96],"multiphysics":[98,237],"approach":[99,300],"feasible,":[100],"it":[101,130],"vital":[103],"to":[104,108,118,137,142,154,159,164,178,197,225,230,293],"find":[105],"admissible":[106],"constraints":[107],"resolve":[109],"uniqueness":[111],"issue":[112],"construct":[119],"good":[121],"boundary":[122,167],"condition":[123,168],"equation":[127,192],"so":[128],"that":[129],"also":[131,291],"becomes":[132],"uniquely":[133],"solvable.":[134],"The":[135,173],"key":[136],"difficulty":[140,157],"discover":[143],"certain":[144],"conserved":[145],"quantities":[146],"solution,":[150],"solution":[153],"second":[156],"use":[160,179],"generate":[165],"problem.":[172],"allows":[176],"any":[180,189],"convergent":[181,190],"Stokes":[182],"solver":[183,193],"(and":[184,194],"its":[185,195],"code)":[186,196],"together":[187],"with":[188,213],"solve":[198],"gel":[201],"In":[203],"paper,":[205],"Taylor\u2013Hood":[207],"mixed":[208],"method":[211,219],"combined":[212],"continuous":[215],"linear":[216],"are":[220,279,290],"chosen":[221],"as":[222],"example":[224],"ideas":[228],"demonstrate":[231],"viability":[233],"proposed":[236,299],"approach.":[238],"It":[239],"proved":[241],"that,":[242],"mesh":[245],"constraint,":[246],"both":[247,282],"semidiscrete":[249,283],"(in":[250],"space)":[251],"enjoy":[256],"energy":[259,265],"laws":[260],"mimic":[262],"differential":[264],"law":[266],"satisfied":[267],"by":[268],"solution.":[271],"Optimal":[272],"order":[273],"error":[274],"estimates":[275],"in":[276],"various":[277],"norms":[278],"established":[280],"methods.":[287,302],"Numerical":[288],"experiments":[289],"presented":[292],"show":[294],"performance":[296]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}