{"id":"https://openalex.org/W2601167827","doi":"https://doi.org/10.1137/16m1091095","title":"Mixed Methods for Two-Phase Darcy--Stokes Mixtures of Partially Melted Materials with Regions of Zero Porosity","display_name":"Mixed Methods for Two-Phase Darcy--Stokes Mixtures of Partially Melted Materials with Regions of Zero Porosity","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2601167827","doi":"https://doi.org/10.1137/16m1091095","mag":"2601167827"},"language":"en","primary_location":{"id":"doi:10.1137/16m1091095","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1091095","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/A5034967156","display_name":"Todd Arbogast","orcid":"https://orcid.org/0000-0001-9692-5478"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Todd Arbogast","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034634594","display_name":"Marc A. Hesse","orcid":"https://orcid.org/0000-0002-2532-3274"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marc A. Hesse","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5025896403","display_name":"Abraham L. Taicher","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Abraham L. Taicher","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":1.604,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.84656216,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"39","issue":"2","first_page":"B375","last_page":"B402"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9995999932289124,"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/T11558","display_name":"Composite Material Mechanics","score":0.9979000091552734,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/darcys-law","display_name":"Darcy's law","score":0.779915988445282},{"id":"https://openalex.org/keywords/stokes-flow","display_name":"Stokes flow","score":0.7052276730537415},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6940410733222961},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.6651221513748169},{"id":"https://openalex.org/keywords/darcy-number","display_name":"Darcy number","score":0.4779006242752075},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46066680550575256},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.4360668659210205},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.426582396030426},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42471301555633545},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.41456297039985657},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.413166344165802},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.338736891746521},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.32994556427001953},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2843914031982422},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.16575485467910767},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15942689776420593},{"id":"https://openalex.org/keywords/reynolds-number","display_name":"Reynolds number","score":0.15685424208641052},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.15562254190444946},{"id":"https://openalex.org/keywords/geotechnical-engineering","display_name":"Geotechnical engineering","score":0.11090320348739624}],"concepts":[{"id":"https://openalex.org/C183447037","wikidata":"https://www.wikidata.org/wiki/Q392416","display_name":"Darcy's law","level":4,"score":0.779915988445282},{"id":"https://openalex.org/C19191322","wikidata":"https://www.wikidata.org/wiki/Q674202","display_name":"Stokes flow","level":3,"score":0.7052276730537415},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6940410733222961},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.6651221513748169},{"id":"https://openalex.org/C2779459783","wikidata":"https://www.wikidata.org/wiki/Q16954269","display_name":"Darcy number","level":5,"score":0.4779006242752075},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46066680550575256},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.4360668659210205},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.426582396030426},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42471301555633545},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.41456297039985657},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.413166344165802},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.338736891746521},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.32994556427001953},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2843914031982422},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.16575485467910767},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15942689776420593},{"id":"https://openalex.org/C182748727","wikidata":"https://www.wikidata.org/wiki/Q178932","display_name":"Reynolds number","level":3,"score":0.15685424208641052},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.15562254190444946},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.11090320348739624},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C130230704","wikidata":"https://www.wikidata.org/wiki/Q898280","display_name":"Nusselt number","level":4,"score":0.0},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1091095","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1091095","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":[{"id":"https://openalex.org/G320633851","display_name":null,"funder_award_id":"EAR-1025321","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4399638168","display_name":null,"funder_award_id":"DMS-1418752","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5128091834","display_name":null,"funder_award_id":"EP/K032208/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8786431655","display_name":null,"funder_award_id":"EP/K032208","funder_id":"https://openalex.org/F4320323243","funder_display_name":"Isaac Newton Institute for Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320323243","display_name":"Isaac Newton Institute for Mathematical Sciences","ror":"https://ror.org/007vkej58"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W46603733","https://openalex.org/W593406250","https://openalex.org/W1492326914","https://openalex.org/W1565627164","https://openalex.org/W1587335451","https://openalex.org/W1601728065","https://openalex.org/W1674659126","https://openalex.org/W1965473425","https://openalex.org/W1966133457","https://openalex.org/W1970934067","https://openalex.org/W1972683041","https://openalex.org/W1983549528","https://openalex.org/W1995682074","https://openalex.org/W1997181819","https://openalex.org/W2015148405","https://openalex.org/W2016534590","https://openalex.org/W2024488576","https://openalex.org/W2049923710","https://openalex.org/W2062002217","https://openalex.org/W2068584896","https://openalex.org/W2077106134","https://openalex.org/W2101438228","https://openalex.org/W2104295992","https://openalex.org/W2120027408","https://openalex.org/W2123069197","https://openalex.org/W2147674969","https://openalex.org/W2159012312","https://openalex.org/W2398884079","https://openalex.org/W2487882368","https://openalex.org/W2530017061","https://openalex.org/W2556087308","https://openalex.org/W3044656254","https://openalex.org/W3103404537","https://openalex.org/W3151825275","https://openalex.org/W4252060206"],"related_works":["https://openalex.org/W1983176903","https://openalex.org/W2385610002","https://openalex.org/W2998664957","https://openalex.org/W1969535115","https://openalex.org/W3146107892","https://openalex.org/W1994780139","https://openalex.org/W2095262078","https://openalex.org/W2270981410","https://openalex.org/W1914317812","https://openalex.org/W14390757"],"abstract_inverted_index":{"The":[0,26],"Earth's":[1],"mantle":[2],"(or,":[3],"e.g.,":[4],"a":[5,8,15,18,31,46,81,136],"glacier)":[6],"involves":[7],"deformable":[9],"solid":[10,41],"matrix":[11,42],"phase":[12],"within":[13],"which":[14],"second":[16],"phase,":[17],"fluid,":[19],"may":[20],"form":[21],"due":[22],"to":[23],"melting":[24],"processes.":[25],"system":[27,62,90,133],"is":[28,63,77,108],"modeled":[29],"as":[30],"dual-continuum":[32],"mixture,":[33],"with":[34],"at":[35],"each":[36],"point":[37],"of":[38,71,88,99,115,149],"space":[39],"the":[40,50,67,75,86,89,94,100,105,147,150],"being":[43,56],"governed":[44,57],"by":[45,58,91,97],"Stokes":[47],"flow":[48],"and":[49,117,134,145],"fluid":[51],"melt,":[52],"if":[53],"it":[54],"exists,":[55],"Darcy's":[59],"law.":[60],"This":[61],"mathematically":[64],"degenerate":[65],"when":[66,111],"porosity":[68,76],"(volume":[69],"fraction":[70],"fluid)":[72],"vanishes.":[73],"Assuming":[74],"given,":[78],"we":[79],"develop":[80,122],"mixed":[82,125],"variational":[83,106],"framework":[84],"for":[85,129],"mechanics":[87],"carefully":[92],"scaling":[93],"Darcy":[95],"variables":[96],"powers":[98],"porosity.":[101],"We":[102,120],"prove":[103,135],"that":[104,143],"problem":[107],"well-posed,":[109],"even":[110],"there":[112],"are":[113,141],"regions":[114],"one":[116],"two":[118],"phases.":[119],"then":[121],"an":[123],"accurate":[124],"finite":[126],"element":[127],"method":[128],"solving":[130],"this":[131],"Darcy--Stokes":[132],"convergence":[137,148],"result.":[138],"Numerical":[139],"results":[140],"presented":[142],"illustrate":[144],"verify":[146],"method.":[151]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":9},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}