{"id":"https://openalex.org/W4205725157","doi":"https://doi.org/10.1090/mcom/3703","title":"Finite element approximation and preconditioning for anisothermal flow of implicitly-constituted non-Newtonian fluids","display_name":"Finite element approximation and preconditioning for anisothermal flow of implicitly-constituted non-Newtonian fluids","publication_year":2021,"publication_date":"2021-09-29","ids":{"openalex":"https://openalex.org/W4205725157","doi":"https://doi.org/10.1090/mcom/3703"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3703","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3703","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://ora.ox.ac.uk/objects/uuid:8526a461-74d6-4a60-9a0e-6d27923a8666","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102855060","display_name":"Patrick E. Farrell","orcid":"https://orcid.org/0000-0002-1241-7060"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Patrick Farrell","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052614625","display_name":"Pablo Alexei Gazca\u2010Orozco","orcid":"https://orcid.org/0000-0001-9859-4238"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE","GB"],"is_corresponding":false,"raw_author_name":"Pablo Alexei Gazca Orozco","raw_affiliation_strings":["Department of Mathematics, FAU Erlangen-N\u00fcrnberg, 91058 Erlangen, Germany","Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, FAU Erlangen-N\u00fcrnberg, 91058 Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]},{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064002486","display_name":"Endre S\u00fcli","orcid":"https://orcid.org/0000-0002-0812-6105"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Endre S\u00fcli","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102855060"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":1.423,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.79758669,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"91","issue":"334","first_page":"659","last_page":"697"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9984999895095825,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9919000267982483,"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/preconditioner","display_name":"Preconditioner","score":0.8776991367340088},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7429582476615906},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.637620210647583},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5897687077522278},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.4700046181678772},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43632084131240845},{"id":"https://openalex.org/keywords/incompressible-flow","display_name":"Incompressible flow","score":0.4235355854034424},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.41016435623168945},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3506423830986023},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.34740930795669556},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.2635881304740906},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15029022097587585},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14347350597381592},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.10338297486305237},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.09731283783912659}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.8776991367340088},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7429582476615906},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.637620210647583},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5897687077522278},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.4700046181678772},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43632084131240845},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.4235355854034424},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.41016435623168945},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3506423830986023},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.34740930795669556},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2635881304740906},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15029022097587585},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14347350597381592},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.10338297486305237},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.09731283783912659}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/mcom/3703","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3703","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:8526a461-74d6-4a60-9a0e-6d27923a8666","is_oa":true,"landing_page_url":null,"pdf_url":"https://ora.ox.ac.uk/objects/uuid:8526a461-74d6-4a60-9a0e-6d27923a8666","source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements","raw_type":"Journal article"}],"best_oa_location":{"id":"pmh:oai:ora.ox.ac.uk:uuid:8526a461-74d6-4a60-9a0e-6d27923a8666","is_oa":true,"landing_page_url":null,"pdf_url":"https://ora.ox.ac.uk/objects/uuid:8526a461-74d6-4a60-9a0e-6d27923a8666","source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements","raw_type":"Journal article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3957501995","display_name":null,"funder_award_id":"EP/R029423/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7295259756","display_name":"PRISM: Platform for Research In Simulation Methods","funder_award_id":"EP/R029423/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4205725157.pdf","grobid_xml":"https://content.openalex.org/works/W4205725157.grobid-xml"},"referenced_works_count":74,"referenced_works":["https://openalex.org/W99114895","https://openalex.org/W209576205","https://openalex.org/W592911714","https://openalex.org/W1585098889","https://openalex.org/W1730744162","https://openalex.org/W1746995274","https://openalex.org/W1895573979","https://openalex.org/W1973212083","https://openalex.org/W1973317191","https://openalex.org/W1975957729","https://openalex.org/W1980053021","https://openalex.org/W1983487891","https://openalex.org/W1986608219","https://openalex.org/W1988719701","https://openalex.org/W1995621805","https://openalex.org/W1996567122","https://openalex.org/W1998046278","https://openalex.org/W2004095151","https://openalex.org/W2005282709","https://openalex.org/W2008192231","https://openalex.org/W2012797268","https://openalex.org/W2017085690","https://openalex.org/W2035814641","https://openalex.org/W2038469131","https://openalex.org/W2041485082","https://openalex.org/W2048525720","https://openalex.org/W2054034220","https://openalex.org/W2054976626","https://openalex.org/W2066870142","https://openalex.org/W2067613252","https://openalex.org/W2070299075","https://openalex.org/W2070308161","https://openalex.org/W2077194775","https://openalex.org/W2080474884","https://openalex.org/W2082606496","https://openalex.org/W2084768159","https://openalex.org/W2084900853","https://openalex.org/W2085581918","https://openalex.org/W2093753671","https://openalex.org/W2110416601","https://openalex.org/W2114164194","https://openalex.org/W2139155801","https://openalex.org/W2160623568","https://openalex.org/W2168522485","https://openalex.org/W2258832456","https://openalex.org/W2263768208","https://openalex.org/W2340656590","https://openalex.org/W2400236714","https://openalex.org/W2507285513","https://openalex.org/W2554006986","https://openalex.org/W2592623476","https://openalex.org/W2611065617","https://openalex.org/W2659701650","https://openalex.org/W2744050773","https://openalex.org/W2790157137","https://openalex.org/W2795984716","https://openalex.org/W2895332762","https://openalex.org/W2913963899","https://openalex.org/W2963357469","https://openalex.org/W2995403156","https://openalex.org/W3007411243","https://openalex.org/W3022172031","https://openalex.org/W3048238488","https://openalex.org/W3096669475","https://openalex.org/W3101410605","https://openalex.org/W3102568135","https://openalex.org/W3104566386","https://openalex.org/W3106000208","https://openalex.org/W3126661955","https://openalex.org/W3139199651","https://openalex.org/W3158687439","https://openalex.org/W4231405723","https://openalex.org/W4244104762","https://openalex.org/W4252104256"],"related_works":["https://openalex.org/W4389317411","https://openalex.org/W1492522302","https://openalex.org/W2096454229","https://openalex.org/W2042199958","https://openalex.org/W2103149966","https://openalex.org/W2177482563","https://openalex.org/W2120298265","https://openalex.org/W2464766188","https://openalex.org/W2016008514","https://openalex.org/W2098174699"],"abstract_inverted_index":{"We":[0,24,40],"devise":[1],"3-field":[2],"and":[3,63,86,102,110],"4-field":[4],"finite":[5,57],"element":[6,58],"approximations":[7,31],"of":[8,15,29,37,75,83],"a":[9,34,42,51,68,76],"system":[10],"describing":[11],"the":[12,27,38,55,61,81,84,100],"steady":[13],"state":[14],"an":[16],"incompressible":[17],"heat-conducting":[18],"fluid":[19],"with":[20],"implicit":[21],"non-Newtonian":[22],"rheology.":[23],"prove":[25],"that":[26,72,79],"sequence":[28],"numerical":[30],"converges":[32],"to":[33,99],"weak":[35],"solution":[36],"problem.":[39],"develop":[41],"block":[43],"preconditioner":[44,66,92],"based":[45,53],"on":[46,54],"augmented":[47],"Lagrangian":[48],"stabilisation":[49],"for":[50,60],"discretisation":[52],"Scott\u2013Vogelius":[56],"pair":[59],"velocity":[62],"pressure.":[64],"The":[65,91],"involves":[67],"specialised":[69],"multigrid":[70],"algorithm":[71],"makes":[73],"use":[74],"space":[77],"decomposition":[78],"captures":[80],"kernel":[82],"divergence":[85],"non-standard":[87],"intergrid":[88],"transfer":[89],"operators.":[90],"exhibits":[93],"robust":[94],"convergence":[95],"behaviour":[96],"when":[97],"applied":[98],"Navier\u2013Stokes":[101],"power-law":[103],"systems,":[104],"including":[105],"temperature-dependent":[106],"viscosity,":[107],"heat":[108],"conductivity":[109],"viscous":[111],"dissipation.":[112]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}