{"id":"https://openalex.org/W2978734802","doi":"https://doi.org/10.1137/19m1237041","title":"Robust Numerical Methods for Nonlocal (and Local) Equations of Porous Medium Type. Part I: Theory","display_name":"Robust Numerical Methods for Nonlocal (and Local) Equations of Porous Medium Type. Part I: Theory","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2978734802","doi":"https://doi.org/10.1137/19m1237041","mag":"2978734802"},"language":"en","primary_location":{"id":"doi:10.1137/19m1237041","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1237041","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11250/2637804","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003056469","display_name":"F\u00e9lix del Teso","orcid":"https://orcid.org/0000-0001-9621-7826"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Felix del Teso","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087229981","display_name":"J\u00f8rgen Endal","orcid":"https://orcid.org/0000-0001-9931-7945"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J\u00f8rgen Endal","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5025746918","display_name":"Espen R. Jakobsen","orcid":"https://orcid.org/0000-0003-4432-1589"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Espen R. Jakobsen","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":5.3578,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.96696768,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"57","issue":"5","first_page":"2266","last_page":"2299"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9988999962806702,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7577944993972778},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.6635348200798035},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6550171375274658},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5282340049743652},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4860589802265167},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.48185834288597107},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4577634930610657},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.43395453691482544},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4255942702293396},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3943136930465698},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36873018741607666},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3671213984489441},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15878665447235107},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14593252539634705},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09032687544822693}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7577944993972778},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.6635348200798035},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6550171375274658},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5282340049743652},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4860589802265167},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.48185834288597107},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4577634930610657},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.43395453691482544},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4255942702293396},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3943136930465698},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36873018741607666},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3671213984489441},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15878665447235107},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14593252539634705},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09032687544822693},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/19m1237041","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1237041","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:bird.bcamath.org:20.500.11824/1161","is_oa":false,"landing_page_url":"http://hdl.handle.net/20.500.11824/1161","pdf_url":null,"source":{"id":"https://openalex.org/S4306401608","display_name":"BIRD (Basque Center for Applied Mathematics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2802176441","host_organization_name":"Basque Center for Applied Mathematics","host_organization_lineage":["https://openalex.org/I2802176441"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:ntnuopen.ntnu.no:11250/2637804","is_oa":true,"landing_page_url":"http://hdl.handle.net/11250/2637804","pdf_url":null,"source":{"id":"https://openalex.org/S4306401716","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2266-2299","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:ntnuopen.ntnu.no:11250/2637804","is_oa":true,"landing_page_url":"http://hdl.handle.net/11250/2637804","pdf_url":null,"source":{"id":"https://openalex.org/S4306401716","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2266-2299","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G942534728","display_name":null,"funder_award_id":"250070","funder_id":"https://openalex.org/F4320323299","funder_display_name":"Norges Forskningsr\u00e5d"}],"funders":[{"id":"https://openalex.org/F4320320885","display_name":"European Research Consortium for Informatics and Mathematics","ror":"https://ror.org/055zrhj18"},{"id":"https://openalex.org/F4320321705","display_name":"Eusko Jaurlaritza","ror":"https://ror.org/00pz2fp31"},{"id":"https://openalex.org/F4320323299","display_name":"Norges Forskningsr\u00e5d","ror":"https://ror.org/00epmv149"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W61439753","https://openalex.org/W1257148767","https://openalex.org/W1967028491","https://openalex.org/W1973254840","https://openalex.org/W1977360274","https://openalex.org/W1984898295","https://openalex.org/W1996308226","https://openalex.org/W1999413164","https://openalex.org/W2005970763","https://openalex.org/W2007927352","https://openalex.org/W2009137576","https://openalex.org/W2010625224","https://openalex.org/W2013828509","https://openalex.org/W2016641115","https://openalex.org/W2016823491","https://openalex.org/W2018865378","https://openalex.org/W2024406524","https://openalex.org/W2024612023","https://openalex.org/W2031097253","https://openalex.org/W2037008679","https://openalex.org/W2039427414","https://openalex.org/W2045118704","https://openalex.org/W2051638496","https://openalex.org/W2063595285","https://openalex.org/W2064830082","https://openalex.org/W2068738591","https://openalex.org/W2070621570","https://openalex.org/W2073691774","https://openalex.org/W2074742922","https://openalex.org/W2083199345","https://openalex.org/W2096035658","https://openalex.org/W2108935063","https://openalex.org/W2123275881","https://openalex.org/W2124303144","https://openalex.org/W2130763970","https://openalex.org/W2133789627","https://openalex.org/W2144844073","https://openalex.org/W2147308762","https://openalex.org/W2154885094","https://openalex.org/W2172034033","https://openalex.org/W2226538084","https://openalex.org/W2318389815","https://openalex.org/W2395085125","https://openalex.org/W2427531423","https://openalex.org/W2587973617","https://openalex.org/W2776342372","https://openalex.org/W2791042172","https://openalex.org/W2963016140","https://openalex.org/W2963176574","https://openalex.org/W2963271176","https://openalex.org/W2963312336","https://openalex.org/W2963745149","https://openalex.org/W2963763304","https://openalex.org/W2963820199","https://openalex.org/W2964340258","https://openalex.org/W3098321018","https://openalex.org/W3101264823","https://openalex.org/W3102842493","https://openalex.org/W3103885682","https://openalex.org/W3123275897","https://openalex.org/W4297968680"],"related_works":["https://openalex.org/W2353039109","https://openalex.org/W2900100504","https://openalex.org/W4315588385","https://openalex.org/W3124638673","https://openalex.org/W2066153363","https://openalex.org/W2061564118","https://openalex.org/W4318566977","https://openalex.org/W4254898719","https://openalex.org/W2146196898","https://openalex.org/W2340858455"],"abstract_inverted_index":{"We":[0,43,195],"develop":[1],"a":[2,28,126,164,229],"unified":[3,127],"and":[4,36,41,103,109,128,135,138,147,170,181,215],"easy":[5],"to":[6,9,48,124,159,206],"use":[7,45],"framework":[8],"study":[10],"robust":[11],"fully":[12],"discrete":[13,107],"numerical":[14,54,199,235],"methods":[15,151,236],"for":[16,51,82,86,105,132],"nonlinear":[17,139],"degenerate":[18,71],"diffusion":[19,31,91,95,140],"equations":[20],"$\\partial_t":[21],"u-\\mathfrak{L}^{\\sigma,\\mu}[\\varphi(u)]=f":[22],"\\;\\text{in}\\;":[23],"\\mathbb{R}^N\\times(0,T),$":[24],"where":[25],"$\\mathfrak{L}^{\\sigma,\\mu}$":[26,97],"is":[27,38,204],"general":[29,171],"symmetric":[30],"operator":[32],"of":[33,61,77,94,149,233],"L\u00e9vy":[34,120],"type":[35],"$\\varphi$":[37],"merely":[39],"continuous":[40],"nondecreasing.":[42],"then":[44],"this":[46],"theory":[47,68,131,143],"prove":[49,167],"convergence":[50,148],"many":[52],"different":[53],"schemes.":[55],"In":[56],"the":[57,62,74,83,99,150,168,207,234],"nonlocal":[58,87,119,130,136],"case":[59],"most":[60],"results":[63],"are":[64,98,118],"completely":[65],"new.":[66],"Our":[67],"covers":[69],"strongly":[70],"Stefan":[72],"problems,":[73,88],"full":[75],"range":[76],"porous":[78],"medium":[79],"equations,":[80],"and,":[81],"first":[84],"time":[85],"also":[89,196],"fast":[90],"equations.":[92,141],"Examples":[93],"operators":[96,117,121],"(fractional)":[100],"Laplacians":[101],"$\\Delta$":[102],"$-(-\\Delta)^{\\frac\\alpha2}$":[104],"$\\alpha\\in(0,2)$,":[106],"operators,":[108],"combinations.":[110],"The":[111,142],"observation":[112],"that":[113,157],"monotone":[114],"finite":[115],"difference":[116],"allows":[122],"us":[123],"give":[125],"compact":[129],"both":[133],"local":[134],"linear":[137],"includes":[144],"stability,":[145],"compactness,":[146],"under":[152],"minimal":[153],"assumptions,":[154],"including":[155],"assumptions":[156],"lead":[158],"very":[160],"irregular":[161],"solutions.":[162],"As":[163],"byproduct,":[165],"we":[166],"new":[169],"existence":[172],"result":[173],"announced":[174],"in":[175,238],"[F.":[176,210],"del":[177,211],"Teso,":[178,212],"J.":[179,213,220],"Endal,":[180,214],"E.":[182,216],"R.":[183,186,217],"Jakobsen,":[184,218],"C.":[185],"Math.":[187],"Acad.":[188],"Sci.":[189],"Paris,":[190],"355":[191],"(2017),":[192],"pp.":[193,225],"1154--1160].":[194],"present":[197],"some":[198],"tests,":[200],"but":[201],"extensive":[202],"testing":[203],"deferred":[205],"companion":[208],"paper":[209],"SIAM":[219],"Numer.":[221],"Anal.,":[222],"56":[223],"(2018),":[224],"3611--3647]":[226],"along":[227],"with":[228],"more":[230],"detailed":[231],"discussion":[232],"included":[237],"our":[239],"theory.":[240]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
