{"id":"https://openalex.org/W2783209822","doi":"https://doi.org/10.1137/17m1112017","title":"On Really Locking-Free Mixed Finite Element Methods for the Transient Incompressible Stokes Equations","display_name":"On Really Locking-Free Mixed Finite Element Methods for the Transient Incompressible Stokes Equations","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2783209822","doi":"https://doi.org/10.1137/17m1112017","mag":"2783209822"},"language":"en","primary_location":{"id":"doi:10.1137/17m1112017","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1112017","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/A5103039267","display_name":"Naveed Ahmed","orcid":"https://orcid.org/0000-0002-9322-0373"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Naveed Ahmed","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024764407","display_name":"Alexander Linke","orcid":"https://orcid.org/0000-0002-0165-2698"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexander Linke","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5080964620","display_name":"Christian Merdon","orcid":"https://orcid.org/0000-0002-3390-2145"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christian Merdon","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5103039267"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4973,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.87998234,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"56","issue":"1","first_page":"185","last_page":"209"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9983999729156494,"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/discretization","display_name":"Discretization","score":0.8063956499099731},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.754488468170166},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.614382266998291},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5571075081825256},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.5339025259017944},{"id":"https://openalex.org/keywords/pressure-correction-method","display_name":"Pressure-correction method","score":0.5290212631225586},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.524676501750946},{"id":"https://openalex.org/keywords/time-derivative","display_name":"Time derivative","score":0.4319838285446167},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.42829155921936035},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35286638140678406},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2006976306438446},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.17493915557861328}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8063956499099731},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.754488468170166},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.614382266998291},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5571075081825256},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.5339025259017944},{"id":"https://openalex.org/C21018558","wikidata":"https://www.wikidata.org/wiki/Q7241680","display_name":"Pressure-correction method","level":3,"score":0.5290212631225586},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.524676501750946},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.4319838285446167},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.42829155921936035},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35286638140678406},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2006976306438446},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.17493915557861328},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/17m1112017","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1112017","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:doi:10.20347/wias.preprint.2368","is_oa":false,"landing_page_url":"http://localhost:8291/receive/wias_mods_00002420","pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"preprint"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1964314926","https://openalex.org/W1970849842","https://openalex.org/W1973212083","https://openalex.org/W1974461496","https://openalex.org/W1987393363","https://openalex.org/W1990281154","https://openalex.org/W2001512608","https://openalex.org/W2005632248","https://openalex.org/W2009818444","https://openalex.org/W2010805011","https://openalex.org/W2014220840","https://openalex.org/W2017319812","https://openalex.org/W2026711180","https://openalex.org/W2040567494","https://openalex.org/W2043605704","https://openalex.org/W2049914863","https://openalex.org/W2051751432","https://openalex.org/W2051862019","https://openalex.org/W2058241749","https://openalex.org/W2072236487","https://openalex.org/W2074716456","https://openalex.org/W2091693457","https://openalex.org/W2118395915","https://openalex.org/W2160623568","https://openalex.org/W2206365535","https://openalex.org/W2215011577","https://openalex.org/W2258832456","https://openalex.org/W2292353766","https://openalex.org/W2400236714","https://openalex.org/W2460241900","https://openalex.org/W2477238223","https://openalex.org/W2507285513","https://openalex.org/W2524024922","https://openalex.org/W2554006986","https://openalex.org/W2556472162","https://openalex.org/W2598994884","https://openalex.org/W2744050773","https://openalex.org/W3022479595","https://openalex.org/W4256651668"],"related_works":["https://openalex.org/W2093607043","https://openalex.org/W1596838038","https://openalex.org/W2416979464","https://openalex.org/W2313597186","https://openalex.org/W1991751407","https://openalex.org/W2328255009","https://openalex.org/W86477321","https://openalex.org/W4233568714","https://openalex.org/W2055092591","https://openalex.org/W1988703624"],"abstract_inverted_index":{"Inf-sup":[0],"stable":[1],"mixed":[2],"methods":[3],"for":[4],"the":[5,12,31,38,41,57,81,84,87,97,104,108,139,147],"steady":[6],"incompressible":[7,99],"Stokes":[8,100],"equations":[9],"that":[10,65],"relax":[11],"divergence":[13],"constraint":[14],"are":[15,128],"often":[16],"claimed":[17],"to":[18,26,37,46,62,96],"deliver":[19],"locking-free":[20],"discretizations.":[21],"However,":[22,51],"this":[23,90,94],"relaxation":[24],"leads":[25,61],"a":[27,47,52,63,121],"pressure-dependent":[28],"contribution":[29],"in":[30,146],"velocity":[32,71,109,123],"error,":[33],"which":[34,130],"is":[35,66,78],"proportional":[36],"inverse":[39],"of":[40,56,80,86,142,149],"viscosity,":[42],"thus":[43],"giving":[44],"rise":[45],"(different)":[48],"locking":[49],"phenomenon.":[50],"recently":[53],"proposed":[54],"modification":[55],"right-hand":[58,105],"side":[59,106],"alone":[60],"discretization":[64],"really":[67],"locking-free;":[68],"i.e.,":[69],"its":[70],"error":[72,126],"converges":[73],"with":[74],"optimal":[75],"order":[76],"and":[77,83,118,124],"independent":[79],"pressure":[82,125],"smallness":[85],"viscosity.":[88],"In":[89],"contribution,":[91],"we":[92],"extend":[93],"approach":[95],"transient":[98],"equations,":[101],"where":[102],"besides":[103],"also":[107],"time":[110],"derivative":[111],"requires":[112],"an":[113],"improved":[114],"space":[115,144],"discretization.":[116],"Semidiscrete":[117],"fully":[119],"discrete":[120],"priori":[122],"estimates":[127],"derived,":[129],"show":[131],"remarkable":[132],"robustness":[133],"properties.":[134],"Two":[135],"numerical":[136],"examples":[137],"illustrate":[138],"superior":[140],"accuracy":[141],"pressure-robust":[143],"discretizations":[145],"case":[148],"small":[150],"viscosities.":[151]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}