{"id":"https://openalex.org/W2005923469","doi":"https://doi.org/10.1137/130938499","title":"On a Multiscale Hybrid-Mixed Method for Advective-Reactive Dominated Problems with Heterogeneous Coefficients","display_name":"On a Multiscale Hybrid-Mixed Method for Advective-Reactive Dominated Problems with Heterogeneous Coefficients","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2005923469","doi":"https://doi.org/10.1137/130938499","mag":"2005923469"},"language":"en","primary_location":{"id":"doi:10.1137/130938499","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130938499","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/A5038482556","display_name":"Christopher Harder","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christopher Harder","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011374809","display_name":"Diego Paredes","orcid":"https://orcid.org/0000-0003-2632-5682"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Diego Paredes","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5059362886","display_name":"Fr\u00e9d\u00e9ric Valentin","orcid":"https://orcid.org/0000-0002-5056-7529"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9ric Valentin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.4513,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.96125589,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"13","issue":"2","first_page":"491","last_page":"518"},"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":0.9998000264167786,"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/T11558","display_name":"Composite Material Mechanics","score":0.9987000226974487,"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/applied-mathematics","display_name":"Applied mathematics","score":0.6297365427017212},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6285450458526611},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.5973057746887207},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5767331123352051},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5741453170776367},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5550652146339417},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5101749897003174},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.5070028305053711},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.4905652403831482},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.4672066569328308},{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.4300910234451294},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34721261262893677},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1931096613407135},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09072068333625793}],"concepts":[{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6297365427017212},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6285450458526611},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.5973057746887207},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5767331123352051},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5741453170776367},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5550652146339417},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5101749897003174},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.5070028305053711},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.4905652403831482},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4672066569328308},{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.4300910234451294},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34721261262893677},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1931096613407135},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09072068333625793},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130938499","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130938499","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6899999976158142,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1975480806","https://openalex.org/W1977096265","https://openalex.org/W1990157709","https://openalex.org/W1993348678","https://openalex.org/W1993393678","https://openalex.org/W1994484297","https://openalex.org/W1995044934","https://openalex.org/W1997640799","https://openalex.org/W2000272165","https://openalex.org/W2014983931","https://openalex.org/W2029918260","https://openalex.org/W2070933671","https://openalex.org/W2073897969","https://openalex.org/W2079925282","https://openalex.org/W2095524611","https://openalex.org/W2104040898","https://openalex.org/W2110320615","https://openalex.org/W2113490770","https://openalex.org/W2129288403","https://openalex.org/W2155879256"],"related_works":["https://openalex.org/W1557607869","https://openalex.org/W2104620528","https://openalex.org/W2366350639","https://openalex.org/W2079401649","https://openalex.org/W4313703117","https://openalex.org/W2757910772","https://openalex.org/W1993738197","https://openalex.org/W2087496541","https://openalex.org/W2028455732","https://openalex.org/W2163017860"],"abstract_inverted_index":{"A":[0],"new":[1,115],"family":[2],"of":[3,38,42,52,58,71,81,97,137,147,159,163],"finite":[4],"element":[5],"methods,":[6],"named":[7],"Multiscale":[8],"Hybrid-Mixed":[9],"method":[10,165],"(or":[11],"MHM":[12],"for":[13,105],"short),":[14],"aims":[15],"to":[16,32,118,168],"solve":[17],"reactive-advective":[18],"dominated":[19],"problems":[20,83,94],"with":[21,84,166],"multiscale":[22,111],"coefficients":[23],"on":[24],"coarse":[25],"meshes.":[26],"The":[27,44],"underlying":[28],"upscaling":[29,45],"procedure":[30],"transfers":[31],"the":[33,36,49,56,59,69,76,79,90,110,138,148,155,161,164,169,173],"basis":[34],"functions":[35],"responsibility":[37],"achieving":[39],"high":[40],"orders":[41],"accuracy.":[43],"is":[46,61],"built":[47],"inside":[48],"general":[50],"framework":[51],"hybridization,":[53],"in":[54],"which":[55,142],"continuity":[57],"solution":[60],"relaxed":[62],"a":[63,101,114,125,127,135],"priori":[64],"and":[65,107,172],"imposed":[66],"weakly":[67],"through":[68],"action":[70],"Lagrange":[72],"multipliers.":[73,91],"This":[74],"characterizes":[75],"unknowns":[77],"as":[78],"solutions":[80],"local":[82,93,121,144],"Robin":[85],"boundary":[86],"conditions":[87],"driven":[88],"by":[89],"Such":[92],"are":[95],"independent":[96],"one":[98],"another,":[99],"yielding":[100],"process":[102],"naturally":[103],"shaped":[104],"parallelization":[106],"adaptivity.":[108],"Moreover,":[109],"decomposition":[112],"indicates":[113],"adaptive":[116],"algorithm":[117],"set":[119],"up":[120],"spaces":[122],"defined":[123],"using":[124],"face-based":[126],"posteriori":[128],"error":[129],"estimator.":[130],"Interestingly,":[131],"it":[132],"also":[133],"embeds":[134],"postprocessing":[136],"dual":[139],"variable":[140],"(flux)":[141],"preserves":[143],"conservation":[145],"properties":[146],"exact":[149],"solution.":[150],"Extensive":[151],"numerical":[152],"validations":[153],"assess":[154],"claimed":[156],"optimal":[157],"rates":[158],"convergence,":[160],"robustness":[162],"respect":[167],"model's":[170],"coefficients,":[171],"adaptivity":[174],"algorithm.":[175]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}