{"id":"https://openalex.org/W2000272165","doi":"https://doi.org/10.1137/060662587","title":"A Multiscale Mortar Mixed Finite Element Method","display_name":"A Multiscale Mortar Mixed Finite Element Method","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2000272165","doi":"https://doi.org/10.1137/060662587","mag":"2000272165"},"language":"en","primary_location":{"id":"doi:10.1137/060662587","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060662587","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling & Simulation","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":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Todd Arbogast","raw_affiliation_strings":["University of Texas at Austin#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Texas at Austin#TAB#","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038648721","display_name":"Gergina Pencheva","orcid":null},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gergina Pencheva","raw_affiliation_strings":["University of Pittsburgh"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Pittsburgh","institution_ids":["https://openalex.org/I170201317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003120570","display_name":"Mary F. Wheeler","orcid":null},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mary F. Wheeler","raw_affiliation_strings":["University of Pittsburgh"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Pittsburgh","institution_ids":["https://openalex.org/I170201317"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008433865","display_name":"Ivan Yotov","orcid":"https://orcid.org/0000-0002-5318-1090"},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ivan Yotov","raw_affiliation_strings":["University of Pittsburgh"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Pittsburgh","institution_ids":["https://openalex.org/I170201317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.4759,"has_fulltext":false,"cited_by_count":303,"citation_normalized_percentile":{"value":0.98679722,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"6","issue":"1","first_page":"319","last_page":"346"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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":1.0,"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":0.9998999834060669,"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":0.9959999918937683,"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/finite-element-method","display_name":"Finite element method","score":0.8043146133422852},{"id":"https://openalex.org/keywords/superconvergence","display_name":"Superconvergence","score":0.642744779586792},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6078375577926636},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5982099771499634},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5849314332008362},{"id":"https://openalex.org/keywords/mortar","display_name":"Mortar","score":0.5570216178894043},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.5302906632423401},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5111232399940491},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5058774352073669},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.4995274543762207},{"id":"https://openalex.org/keywords/mortar-methods","display_name":"Mortar methods","score":0.4936846196651459},{"id":"https://openalex.org/keywords/extended-finite-element-method","display_name":"Extended finite element method","score":0.49088579416275024},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4176608920097351},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.393026202917099},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.383478045463562},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21508446335792542},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08668312430381775},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.08457225561141968}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.8043146133422852},{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.642744779586792},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6078375577926636},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5982099771499634},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5849314332008362},{"id":"https://openalex.org/C130767629","wikidata":"https://www.wikidata.org/wiki/Q7905205","display_name":"Mortar","level":2,"score":0.5570216178894043},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.5302906632423401},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5111232399940491},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5058774352073669},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.4995274543762207},{"id":"https://openalex.org/C97110765","wikidata":"https://www.wikidata.org/wiki/Q17099078","display_name":"Mortar methods","level":4,"score":0.4936846196651459},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.49088579416275024},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4176608920097351},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.393026202917099},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.383478045463562},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21508446335792542},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08668312430381775},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.08457225561141968},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/060662587","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060662587","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling & Simulation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.140.2773","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.140.2773","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.pitt.edu/techrep/0615.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.80.4052","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.80.4052","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.pitt.edu/~yotov/research/publications/msmortar-siam.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.4000000059604645}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W21601394","https://openalex.org/W46603733","https://openalex.org/W81385328","https://openalex.org/W136185420","https://openalex.org/W1545082185","https://openalex.org/W1586623601","https://openalex.org/W1597209545","https://openalex.org/W1852082788","https://openalex.org/W1866311589","https://openalex.org/W1966480196","https://openalex.org/W1966922361","https://openalex.org/W1983736959","https://openalex.org/W1995682074","https://openalex.org/W1997640799","https://openalex.org/W2003637147","https://openalex.org/W2005788407","https://openalex.org/W2009985306","https://openalex.org/W2010194973","https://openalex.org/W2014126302","https://openalex.org/W2020347382","https://openalex.org/W2023515318","https://openalex.org/W2024054122","https://openalex.org/W2024798661","https://openalex.org/W2029918260","https://openalex.org/W2032730144","https://openalex.org/W2034532318","https://openalex.org/W2040933131","https://openalex.org/W2041523977","https://openalex.org/W2051682834","https://openalex.org/W2059321831","https://openalex.org/W2061172735","https://openalex.org/W2062618977","https://openalex.org/W2067510987","https://openalex.org/W2070033465","https://openalex.org/W2078045751","https://openalex.org/W2082599981","https://openalex.org/W2094875449","https://openalex.org/W2113227897","https://openalex.org/W2464997744","https://openalex.org/W2491027544","https://openalex.org/W2491537644","https://openalex.org/W2934526567","https://openalex.org/W3149667697","https://openalex.org/W4239299544"],"related_works":["https://openalex.org/W1567939749","https://openalex.org/W111458089","https://openalex.org/W2754378663","https://openalex.org/W2005628797","https://openalex.org/W1977906733","https://openalex.org/W2011851063","https://openalex.org/W2010821947","https://openalex.org/W2064360755","https://openalex.org/W2370147615","https://openalex.org/W2313299170"],"abstract_inverted_index":{"We":[0,96,128],"develop":[1],"multiscale":[2,89,94],"mortar":[3,21,51,61,109,152],"mixed":[4],"finite":[5,22,90],"element":[6,23,91],"discretizations":[7],"for":[8,121],"second":[9],"order":[10,77,112],"elliptic":[11],"equations.":[12],"The":[13,46],"continuity":[14],"of":[15,49,107,160],"flux":[16],"is":[17,81],"imposed":[18],"via":[19],"a":[20,26,42,98,134],"space":[24,62],"on":[25,41,70,117],"coarse":[27,35,72],"grid":[28,44,73],"scale,":[29],"while":[30],"the":[31,34,50,60,67,108,118,123,161],"equations":[32],"in":[33,58,141,158],"elements":[36],"(or":[37],"subdomains)":[38],"are":[39,139,156],"discretized":[40],"fine":[43,68,119],"scale.":[45],"polynomial":[47],"degree":[48],"and":[52,92,102,114,125,132,151],"subdomain":[53,150],"approximation":[54,64],"spaces":[55],"may":[56],"differ;":[57],"fact,":[59],"achieves":[63],"comparable":[65],"to":[66,147],"scale":[69,120],"its":[71,126],"by":[74],"using":[75],"higher":[76],"polynomials.":[78],"Our":[79],"formulation":[80],"related":[82],"to,":[83],"but":[84],"more":[85],"flexible":[86],"than,":[87],"existing":[88],"variational":[93],"methods.":[95],"derive":[97,130],"priori":[99],"error":[100,136],"estimates":[101],"show,":[103],"with":[104],"appropriate":[105,149],"choice":[106],"space,":[110],"optimal":[111],"convergence":[113],"some":[115],"superconvergence":[116],"both":[122],"solution":[124],"flux.":[127],"also":[129],"efficient":[131],"reliable":[133],"posteriori":[135],"estimators,":[137],"which":[138],"used":[140],"an":[142],"adaptive":[143],"mesh":[144],"refinement":[145],"algorithm":[146],"obtain":[148],"grids.":[153],"Numerical":[154],"experiments":[155],"presented":[157],"confirmation":[159],"theory.":[162]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":22},{"year":2021,"cited_by_count":20},{"year":2020,"cited_by_count":24},{"year":2019,"cited_by_count":28},{"year":2018,"cited_by_count":23},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":14},{"year":2014,"cited_by_count":23},{"year":2013,"cited_by_count":19},{"year":2012,"cited_by_count":15}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}