{"id":"https://openalex.org/W1980076855","doi":"https://doi.org/10.1137/s0036142900378406","title":"Sharp<i>L</i><sup>2</sup>-Error Estimates and Superconvergence of Mixed Finite Element Methods for Non-Fickian Flows in Porous Media","display_name":"Sharp<i>L</i><sup>2</sup>-Error Estimates and Superconvergence of Mixed Finite Element Methods for Non-Fickian Flows in Porous Media","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1980076855","doi":"https://doi.org/10.1137/s0036142900378406","mag":"1980076855"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142900378406","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142900378406","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/A5112526925","display_name":"Richard E. Ewing","orcid":null},"institutions":[{"id":"https://openalex.org/I2801613365","display_name":"Mitchell Institute","ror":"https://ror.org/03ds72003","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I2801613365"]},{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard E. Ewing","raw_affiliation_strings":["Texas A&M University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas A&M University","institution_ids":["https://openalex.org/I2801613365","https://openalex.org/I91045830"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100845665","display_name":"Yanping Lin","orcid":null},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Yanping Lin.","raw_affiliation_strings":["University of Alberta"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Alberta","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108397134","display_name":"Tong Sun.","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tong Sun.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002748671","display_name":"Junping Wang.","orcid":null},"institutions":[{"id":"https://openalex.org/I167576493","display_name":"Colorado School of Mines","ror":"https://ror.org/04raf6v53","country_code":"US","type":"education","lineage":["https://openalex.org/I167576493"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Junping Wang.","raw_affiliation_strings":["Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, CO 80401"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, CO 80401","institution_ids":["https://openalex.org/I167576493"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100394795","display_name":"Shuhua Zhang","orcid":"https://orcid.org/0000-0003-1572-0804"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shuhua Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4647,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.63087324,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"40","issue":"4","first_page":"1538","last_page":"1560"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9972000122070312,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9945999979972839,"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/superconvergence","display_name":"Superconvergence","score":0.9160698652267456},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8014301657676697},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5950019955635071},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.582554817199707},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5484288334846497},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5339576005935669},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.48106884956359863},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.432763934135437},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.337885320186615},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3282780945301056},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.14090868830680847},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13284200429916382},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.090412437915802},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.07925626635551453}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.9160698652267456},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8014301657676697},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5950019955635071},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.582554817199707},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5484288334846497},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5339576005935669},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.48106884956359863},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.432763934135437},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.337885320186615},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3282780945301056},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.14090868830680847},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13284200429916382},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.090412437915802},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.07925626635551453},{"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/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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":1,"locations":[{"id":"doi:10.1137/s0036142900378406","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142900378406","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1122161438","display_name":null,"funder_award_id":"INT-9901498","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1762023238","display_name":"Mathematical Sciences:  Innovative Finite Element Methods   for Modeling Multiphase Contaminant Flows in Porous Media","funder_award_id":"9626179","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2708336614","display_name":"Innovative Finite Element Methods for Modeling Multiphase Contaminant Flows in Porous Media","funder_award_id":"9972147","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3977642034","display_name":"U.S.- China Coperative Research: Numerical Methods and their Application to Computer Simulation of Flows in Underground Reservoirs","funder_award_id":"9901498","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4287666037","display_name":"vBNS Connectivity for Texas A&M University","funder_award_id":"9710337","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4528415245","display_name":"Mathematical Sciences Computing Research Environments","funder_award_id":"9707930","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5615264832","display_name":null,"funder_award_id":"DMS-9626179","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7785058844","display_name":null,"funder_award_id":"DMS-9972147","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320308138","display_name":"Texas Higher Education Coordinating Board","ror":"https://ror.org/05as1qb59"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W71487156","https://openalex.org/W73179330","https://openalex.org/W136185420","https://openalex.org/W204801424","https://openalex.org/W1852082788","https://openalex.org/W1964925308","https://openalex.org/W1971545299","https://openalex.org/W1981363793","https://openalex.org/W1983486085","https://openalex.org/W1986267641","https://openalex.org/W1988234876","https://openalex.org/W1995151111","https://openalex.org/W1996727835","https://openalex.org/W2009188658","https://openalex.org/W2010194973","https://openalex.org/W2020872426","https://openalex.org/W2025944808","https://openalex.org/W2030520530","https://openalex.org/W2033672550","https://openalex.org/W2043950820","https://openalex.org/W2047378168","https://openalex.org/W2049571296","https://openalex.org/W2051313269","https://openalex.org/W2057646856","https://openalex.org/W2058902234","https://openalex.org/W2061172735","https://openalex.org/W2082621526","https://openalex.org/W2083554239","https://openalex.org/W2157468756","https://openalex.org/W2182492950","https://openalex.org/W2331941476","https://openalex.org/W2523474032","https://openalex.org/W2586478169","https://openalex.org/W3118478457","https://openalex.org/W3149667697","https://openalex.org/W4247711213"],"related_works":["https://openalex.org/W2094577950","https://openalex.org/W2031157121","https://openalex.org/W1565666028","https://openalex.org/W2891538916","https://openalex.org/W2160252404","https://openalex.org/W4230524683","https://openalex.org/W3141012097","https://openalex.org/W185121461","https://openalex.org/W1968948586","https://openalex.org/W2074037040"],"abstract_inverted_index":{"A":[0],"sharper":[1],"L2":[2,51,82],"-error":[3],"estimate":[4],"is":[5,68,90],"obtained":[6],"for":[7,53,61,70,84,115],"the":[8,25,54,57,62,65,71,77,85,88,101,104],"non-Fickian":[9],"flow":[10],"of":[11,18,24,95,103],"fluid":[12],"in":[13,30],"porous":[14],"media":[15],"by":[16,93],"means":[17],"a":[19,109],"mixed":[20,26,72,117],"Ritz--Volterra":[21,78],"projection":[22,28],"instead":[23],"Ritz":[27],"used":[29],"[R.":[31],"E.":[32],"Ewing,":[33],"Y.":[34],"Lin,":[35],"and":[36,60,80,87],"J.":[37],"Wang,":[38],"Acta":[39],"Math.":[40],"Univ.":[41],"Comenian.":[42],"(":[43],"N.S.),":[44],"70":[45],"(2001),":[46],"pp.":[47],"75--84].":[48],"Moreover,":[49],"local":[50],"superconvergence":[52,83,105],"velocity":[55,86],"along":[56],"Gauss":[58,66],"lines":[59],"pressure":[63,89],"at":[64],"points":[67],"derived":[69],"finite":[73,118],"element":[74,119],"method":[75],"via":[76],"projection,":[79],"global":[81],"also":[91],"investigated":[92],"virtue":[94],"an":[96],"interpolation":[97],"postprocessing":[98],"technique.":[99],"On":[100],"basis":[102],"estimates,":[106],"some":[107],"useful":[108],"posteriori":[110],"error":[111],"estimators":[112],"are":[113],"presented":[114],"this":[116],"method.":[120]},"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":20}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}