{"id":"https://openalex.org/W2081517630","doi":"https://doi.org/10.1137/s0036142998335698","title":"Positivity-Preserving Numerical Schemes for Lubrication-Type Equations","display_name":"Positivity-Preserving Numerical Schemes for Lubrication-Type Equations","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2081517630","doi":"https://doi.org/10.1137/s0036142998335698","mag":"2081517630"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142998335698","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142998335698","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/A5039058738","display_name":"Liya Zhornitskaya","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L. Zhornitskaya","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5090707978","display_name":"Andrea L. Bertozzi","orcid":"https://orcid.org/0000-0003-0396-7391"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. L. Bertozzi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.3143,"has_fulltext":false,"cited_by_count":162,"citation_normalized_percentile":{"value":0.97688111,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"37","issue":"2","first_page":"523","last_page":"555"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.9995999932289124,"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/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.9995999932289124,"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/T11379","display_name":"Rheology and Fluid Dynamics Studies","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/1507","display_name":"Fluid Flow and Transfer Processes"},"field":{"id":"https://openalex.org/fields/15","display_name":"Chemical 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":0.9934999942779541,"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":0.7640179395675659},{"id":"https://openalex.org/keywords/nabla-symbol","display_name":"Nabla symbol","score":0.6229211091995239},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5654730796813965},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5424363017082214},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.5126213431358337},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.49715450406074524},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.47703880071640015},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4573005139827728},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.4542733132839203},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.4527391195297241},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.45221248269081116},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.44867751002311707},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.43491053581237793},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3851228356361389},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13493916392326355}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7640179395675659},{"id":"https://openalex.org/C54207081","wikidata":"https://www.wikidata.org/wiki/Q937750","display_name":"Nabla symbol","level":3,"score":0.6229211091995239},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5654730796813965},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5424363017082214},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5126213431358337},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.49715450406074524},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.47703880071640015},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4573005139827728},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.4542733132839203},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4527391195297241},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.45221248269081116},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.44867751002311707},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.43491053581237793},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3851228356361389},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13493916392326355},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142998335698","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142998335698","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:CiteSeerX.psu:10.1.1.52.4280","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.4280","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.duke.edu/faculty/bertozzi/SINUM.ps","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":21,"referenced_works":["https://openalex.org/W191309704","https://openalex.org/W1532153246","https://openalex.org/W1970380607","https://openalex.org/W1977106683","https://openalex.org/W1998136115","https://openalex.org/W2006580718","https://openalex.org/W2008209583","https://openalex.org/W2011723842","https://openalex.org/W2012804067","https://openalex.org/W2027518817","https://openalex.org/W2048285539","https://openalex.org/W2055388805","https://openalex.org/W2058436955","https://openalex.org/W2073114034","https://openalex.org/W2076582418","https://openalex.org/W2078279585","https://openalex.org/W2080603656","https://openalex.org/W2083250674","https://openalex.org/W2115619789","https://openalex.org/W4235891758","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2225538548","https://openalex.org/W3114130132","https://openalex.org/W2091671071","https://openalex.org/W2265097382","https://openalex.org/W2517053368","https://openalex.org/W1697484951","https://openalex.org/W2050401359","https://openalex.org/W4297084911","https://openalex.org/W1590663584","https://openalex.org/W3166395799"],"abstract_inverted_index":{".":[0],"Lubrication":[1],"equations":[2,8,51],"are":[3],"fourth":[4],"order":[5],"degenerate":[6],"diffusion":[7],"of":[9,32,44,71,109,113],"the":[10,45,68,72,86,110,114,118,128,135],"form":[11],"h":[12,36],"t":[13],"+":[14],"r":[15],"\\\\Delta":[16],"(f(h)r\\\\Deltah)":[17],"=":[18],"0,":[19],"describing":[20,42],"thin":[21],"films":[22],"or":[23],"liquid":[24],"layers":[25],"driven":[26],"by":[27],"surface":[28],"tension.":[29],"Recent":[30],"studies":[31],"singularities":[33],"in":[34,100],"which":[35,55],"!":[37],"0":[38],"at":[39],"a":[40,77,122],"point,":[41],"rupture":[43],"fluid":[46],"layer,":[47],"show":[48,76,126],"that":[49,67,106,127,147],"such":[50,90,121],"exhibit":[52],"complex":[53],"dynamics":[54],"can":[56,130],"be":[57,142],"difficult":[58],"to":[59,88,141],"simulate":[60],"accurately.":[61],"In":[62],"particular,":[63],"one":[64,101],"must":[65],"ensure":[66],"numerical":[69,98],"approximation":[70],"interface":[73],"does":[74],"not":[75],"false":[78],"premature":[79],"rupture.":[80],"Generic":[81],"finite":[82,150],"difference":[83,151],"schemes":[84,129,152],"have":[85,153],"potential":[87],"manifest":[89],"instabilities":[91],"especially":[92],"when":[93,134],"under-resolved.":[94],"We":[95,124,145],"present":[96],"new":[97],"methods,":[99],"and":[102],"two":[103],"space":[104],"dimensions,":[105],"preserve":[107,131],"positivity":[108,132,148],"solution,":[111],"regardless":[112],"spatial":[115],"resolution,":[116],"whenever":[117],"PDE":[119,136],"has":[120],"property.":[123],"also":[125],"even":[133],"itself":[137],"is":[138],"only":[139],"known":[140],"nonnegativity":[143],"preserving.":[144],"prove":[146],"preserving":[149],"uniqu...":[154]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":13},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
