{"id":"https://openalex.org/W1985843599","doi":"https://doi.org/10.1137/110825960","title":"Recent Developments in Numerical Methods for Fully Nonlinear Second Order Partial Differential Equations","display_name":"Recent Developments in Numerical Methods for Fully Nonlinear Second Order Partial Differential Equations","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1985843599","doi":"https://doi.org/10.1137/110825960","mag":"1985843599"},"language":"en","primary_location":{"id":"doi:10.1137/110825960","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110825960","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","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/A5011365911","display_name":"Xiaobing Feng","orcid":"https://orcid.org/0000-0002-9191-9092"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaobing Feng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056887719","display_name":"Roland Glowinski","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Roland Glowinski","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039552338","display_name":"Michael Neilan","orcid":"https://orcid.org/0000-0002-1564-1041"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Neilan","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":16.9191,"has_fulltext":false,"cited_by_count":130,"citation_normalized_percentile":{"value":0.99557255,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"55","issue":"2","first_page":"205","last_page":"267"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998000264167786,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9977999925613403,"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/partial-differential-equation","display_name":"Partial differential equation","score":0.7656707167625427},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7184344530105591},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5638583302497864},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47090959548950195},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.4663284122943878},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43628495931625366},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4251103699207306},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3651497960090637},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21955528855323792},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12239006161689758}],"concepts":[{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.7656707167625427},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7184344530105591},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5638583302497864},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47090959548950195},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.4663284122943878},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43628495931625366},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4251103699207306},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3651497960090637},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21955528855323792},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12239006161689758},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","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/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110825960","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110825960","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure","score":0.4300000071525574}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":111,"referenced_works":["https://openalex.org/W153353184","https://openalex.org/W1482716611","https://openalex.org/W1526719111","https://openalex.org/W1558410597","https://openalex.org/W1775501378","https://openalex.org/W1964000054","https://openalex.org/W1964377184","https://openalex.org/W1964753390","https://openalex.org/W1966370580","https://openalex.org/W1967021195","https://openalex.org/W1968373396","https://openalex.org/W1969768229","https://openalex.org/W1971148501","https://openalex.org/W1971839862","https://openalex.org/W1975544169","https://openalex.org/W1975738182","https://openalex.org/W1977440328","https://openalex.org/W1978507854","https://openalex.org/W1980372935","https://openalex.org/W1980835848","https://openalex.org/W1981760129","https://openalex.org/W1985506636","https://openalex.org/W1988044952","https://openalex.org/W1988420172","https://openalex.org/W1988747288","https://openalex.org/W1989136682","https://openalex.org/W1989877076","https://openalex.org/W1994986764","https://openalex.org/W1995499542","https://openalex.org/W1999545889","https://openalex.org/W2000242689","https://openalex.org/W2002182424","https://openalex.org/W2002707718","https://openalex.org/W2004745280","https://openalex.org/W2005448420","https://openalex.org/W2005919860","https://openalex.org/W2008251515","https://openalex.org/W2009259073","https://openalex.org/W2009863089","https://openalex.org/W2011600769","https://openalex.org/W2012999285","https://openalex.org/W2015368117","https://openalex.org/W2016551687","https://openalex.org/W2019270511","https://openalex.org/W2024969615","https://openalex.org/W2027438381","https://openalex.org/W2036476462","https://openalex.org/W2036759661","https://openalex.org/W2038246176","https://openalex.org/W2049391017","https://openalex.org/W2052424080","https://openalex.org/W2054715051","https://openalex.org/W2054829223","https://openalex.org/W2055148892","https://openalex.org/W2055207932","https://openalex.org/W2055341194","https://openalex.org/W2055752660","https://openalex.org/W2057462050","https://openalex.org/W2057938834","https://openalex.org/W2059686907","https://openalex.org/W2061449874","https://openalex.org/W2068875595","https://openalex.org/W2069726223","https://openalex.org/W2072417773","https://openalex.org/W2075869990","https://openalex.org/W2076694827","https://openalex.org/W2077827311","https://openalex.org/W2078167885","https://openalex.org/W2079115983","https://openalex.org/W2081099228","https://openalex.org/W2084358734","https://openalex.org/W2088491967","https://openalex.org/W2090631690","https://openalex.org/W2092046358","https://openalex.org/W2095120409","https://openalex.org/W2098745223","https://openalex.org/W2099707953","https://openalex.org/W2101823897","https://openalex.org/W2116442609","https://openalex.org/W2120290852","https://openalex.org/W2122180808","https://openalex.org/W2125671914","https://openalex.org/W2132003031","https://openalex.org/W2132883347","https://openalex.org/W2133276356","https://openalex.org/W2137824888","https://openalex.org/W2138794399","https://openalex.org/W2139301315","https://openalex.org/W2145754040","https://openalex.org/W2145859152","https://openalex.org/W2147555557","https://openalex.org/W2148823781","https://openalex.org/W2149747548","https://openalex.org/W2154185329","https://openalex.org/W2155324103","https://openalex.org/W2162323386","https://openalex.org/W2165512200","https://openalex.org/W2171076800","https://openalex.org/W2177195156","https://openalex.org/W2313087217","https://openalex.org/W2324428477","https://openalex.org/W2330394843","https://openalex.org/W2335457376","https://openalex.org/W2524112160","https://openalex.org/W2588998037","https://openalex.org/W2726239548","https://openalex.org/W2749408143","https://openalex.org/W3099267538","https://openalex.org/W4237718706","https://openalex.org/W4244294636","https://openalex.org/W4292363360"],"related_works":["https://openalex.org/W2075755912","https://openalex.org/W2148349605","https://openalex.org/W2091296067","https://openalex.org/W2070999895","https://openalex.org/W2085522030","https://openalex.org/W2883804816","https://openalex.org/W4290062051","https://openalex.org/W2114275337","https://openalex.org/W1977112452","https://openalex.org/W2329254523"],"abstract_inverted_index":{"This":[0,106],"article":[1,107],"surveys":[2],"the":[3,79,96,118],"recent":[4],"developments":[5],"in":[6,31,40,95,125],"computational":[7],"methods":[8,127],"for":[9,90,128],"second":[10,68],"order":[11,69],"fully":[12,66,129],"nonlinear":[13,67,130],"partial":[14],"differential":[15,35],"equations":[16],"(PDEs),":[17],"a":[18,73],"relatively":[19],"new":[20,115],"subarea":[21],"within":[22],"numerical":[23,63,80,126],"PDEs.":[24,131],"Due":[25],"to":[26,65,109,117],"their":[27],"ever":[28],"increasing":[29],"importance":[30],"mathematics":[32],"itself":[33],"(e.g.,":[34,46],"geometry":[36],"and":[37,39,43,60,82,114,121],"PDEs)":[38],"many":[41,101],"scientific":[42,83],"engineering":[44],"fields":[45],"astrophysics,":[47],"geostrophic":[48],"fluid":[49],"dynamics,":[50],"grid":[51],"generation,":[52],"image":[53],"processing,":[54],"optimal":[55,61],"transport,":[56],"meteorology,":[57],"mathematical":[58],"finance,":[59],"control),":[62],"solutions":[64],"PDEs":[70],"have":[71],"garnered":[72],"great":[74],"deal":[75],"of":[76,93],"interest":[77,124],"from":[78],"PDE":[81],"communities.":[84],"Significant":[85],"progress":[86],"has":[87],"been":[88],"made":[89],"this":[91],"class":[92],"problems":[94,102],"past":[97],"few":[98],"years,":[99],"but":[100],"still":[103],"remain":[104],"open.":[105],"intends":[108],"introduce":[110],"these":[111],"current":[112],"advancements":[113],"results":[116],"SIAM":[119],"community":[120],"generate":[122],"more":[123]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":7}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
