{"id":"https://openalex.org/W2064076233","doi":"https://doi.org/10.1137/s0036142903428281","title":"An Optimal-Order Error Estimate for a Family of ELLAM-MFEM Approximations to Porous Medium Flow","display_name":"An Optimal-Order Error Estimate for a Family of ELLAM-MFEM Approximations to Porous Medium Flow","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2064076233","doi":"https://doi.org/10.1137/s0036142903428281","mag":"2064076233"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142903428281","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903428281","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/A5100370931","display_name":"Hong Wang","orcid":"https://orcid.org/0000-0002-5125-9974"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hong Wang","raw_affiliation_strings":["hwang@math.sc.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"hwang@math.sc.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100370931"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.292,"has_fulltext":false,"cited_by_count":57,"citation_normalized_percentile":{"value":0.88158331,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"46","issue":"4","first_page":"2133","last_page":"2152"},"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":0.9994999766349792,"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":0.9994999766349792,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9993000030517578,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9961000084877014,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8082269430160522},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5687124133110046},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.5551278591156006},{"id":"https://openalex.org/keywords/spurious-relationship","display_name":"Spurious relationship","score":0.5469165444374084},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5308870673179626},{"id":"https://openalex.org/keywords/eulerian-path","display_name":"Eulerian path","score":0.5213814377784729},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5124278664588928},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.49617037177085876},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4715029299259186},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.45511844754219055},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44700857996940613},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.43192344903945923},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.20532530546188354},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.16725996136665344},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1592286229133606}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8082269430160522},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5687124133110046},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.5551278591156006},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.5469165444374084},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5308870673179626},{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.5213814377784729},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5124278664588928},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.49617037177085876},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4715029299259186},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.45511844754219055},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44700857996940613},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.43192344903945923},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.20532530546188354},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.16725996136665344},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1592286229133606},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142903428281","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903428281","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"},{"id":"pmh:oai:scholarcommons.sc.edu:math_facpub-1064","is_oa":false,"landing_page_url":"https://scholarcommons.sc.edu/math_facpub/69","pdf_url":null,"source":{"id":"https://openalex.org/S4306401386","display_name":"Scholar Commons (University of South Carolina)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I155781252","host_organization_name":"University of South Carolina","host_organization_lineage":["https://openalex.org/I155781252"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W204624611","https://openalex.org/W336569389","https://openalex.org/W1583880678","https://openalex.org/W1708679080","https://openalex.org/W1972490849","https://openalex.org/W1980787167","https://openalex.org/W1986626836","https://openalex.org/W1986678633","https://openalex.org/W1989989318","https://openalex.org/W2011860419","https://openalex.org/W2022390295","https://openalex.org/W2024625961","https://openalex.org/W2028110131","https://openalex.org/W2028230944","https://openalex.org/W2031441801","https://openalex.org/W2033783682","https://openalex.org/W2037368175","https://openalex.org/W2041496706","https://openalex.org/W2041523977","https://openalex.org/W2043273616","https://openalex.org/W2044670314","https://openalex.org/W2047378168","https://openalex.org/W2065874602","https://openalex.org/W2071077032","https://openalex.org/W2082621526","https://openalex.org/W2088575302","https://openalex.org/W2124963644","https://openalex.org/W2523474032","https://openalex.org/W4252264888","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2162899405","https://openalex.org/W3113091479","https://openalex.org/W941090075","https://openalex.org/W2044987316","https://openalex.org/W2237480245","https://openalex.org/W3134374554","https://openalex.org/W2519167559","https://openalex.org/W2075065631","https://openalex.org/W4288358396","https://openalex.org/W2091480169"],"abstract_inverted_index":{"Mathematical":[0],"models":[1],"used":[2,56,70],"to":[3,9,28,57],"describe":[4],"porous":[5,76],"medium":[6,77],"flow":[7,78],"lead":[8],"coupled":[10],"systems":[11],"of":[12,102],"time-dependent":[13],"nonlinear":[14],"partial":[15],"differential":[16],"equations,":[17],"which":[18,48],"present":[19],"serious":[20],"mathematical":[21],"and":[22,62,85],"numerical":[23,30,36],"difficulties.":[24],"Standard":[25],"methods":[26],"tend":[27],"generate":[29],"solutions":[31],"with":[32,39],"nonphysical":[33],"oscillations":[34],"or":[35],"dispersion":[37],"along":[38],"spurious":[40],"grid-orientation":[41],"effect.":[42],"The":[43],"ELLAM-MFEM":[44,103],"time-stepping":[45],"procedure,":[46],"in":[47],"an":[49,95],"Eulerian\u2013Lagrangian":[50],"localized":[51],"adjoint":[52],"method":[53,67],"(ELLAM)":[54],"is":[55,69],"solve":[58],"the":[59,72],"transport":[60],"equation":[61],"a":[63,100],"mixed":[64],"finite":[65],"element":[66],"(MFEM)":[68],"for":[71,99],"pressure":[73],"equation,":[74],"simulates":[75],"accurately":[79],"even":[80],"if":[81],"large":[82],"spatial":[83],"grids":[84],"time":[86],"steps":[87],"are":[88],"used.":[89],"In":[90],"this":[91],"paper":[92],"we":[93],"prove":[94],"optimal-order":[96],"error":[97],"estimate":[98],"family":[101],"approximations.":[104]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
