{"id":"https://openalex.org/W3006204015","doi":"https://doi.org/10.1137/19m1296720","title":"Asymptotically Compatible Schemes for Robust Discretization of Parametrized Problems with Applications to Nonlocal Models","display_name":"Asymptotically Compatible Schemes for Robust Discretization of Parametrized Problems with Applications to Nonlocal Models","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3006204015","doi":"https://doi.org/10.1137/19m1296720","mag":"3006204015"},"language":"en","primary_location":{"id":"doi:10.1137/19m1296720","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1296720","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/A5078205547","display_name":"Xiaochuan Tian","orcid":"https://orcid.org/0000-0002-4539-6702"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaochuan Tian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5056115552","display_name":"Qiang Du","orcid":"https://orcid.org/0000-0002-1067-8937"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qiang Du","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-1067-8937","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5061,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.93553669,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"62","issue":"1","first_page":"199","last_page":"227"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9991999864578247,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9983999729156494,"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/discretization","display_name":"Discretization","score":0.8250725269317627},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.671530544757843},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6122218370437622},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5968150496482849},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5748891830444336},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5664293766021729},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.4590313732624054},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33471518754959106},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3218749165534973},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10297015309333801}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8250725269317627},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.671530544757843},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6122218370437622},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5968150496482849},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5748891830444336},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5664293766021729},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.4590313732624054},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33471518754959106},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3218749165534973},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10297015309333801},{"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:10.1137/19m1296720","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1296720","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":[],"awards":[{"id":"https://openalex.org/G4946931266","display_name":null,"funder_award_id":"W911NF\u201015\u20101\u20100562","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"},{"id":"https://openalex.org/G5202905365","display_name":"Numerical Analysis of Smoothed Particle Hydrodynamics Type Methods via  Nonlocal Models","funder_award_id":"1719699","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6081138888","display_name":"Mathematical Analysis and Numerical Methods for Peridynamics and Nonlocal Models","funder_award_id":"1819233","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8398478472","display_name":"GOALI: Collaborative Research: Model-Predictive Safety Systems for Predictive Detection of Operation Hazards","funder_award_id":"1704833","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/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W1569512514","https://openalex.org/W1968883510","https://openalex.org/W1973127220","https://openalex.org/W1974725498","https://openalex.org/W1977835576","https://openalex.org/W1982427175","https://openalex.org/W1985849851","https://openalex.org/W1986784896","https://openalex.org/W1993215954","https://openalex.org/W1993930468","https://openalex.org/W2001032670","https://openalex.org/W2001730319","https://openalex.org/W2006044588","https://openalex.org/W2008086878","https://openalex.org/W2011095781","https://openalex.org/W2012828992","https://openalex.org/W2023102307","https://openalex.org/W2029529153","https://openalex.org/W2034586897","https://openalex.org/W2036662074","https://openalex.org/W2056885095","https://openalex.org/W2063253250","https://openalex.org/W2064845551","https://openalex.org/W2068276211","https://openalex.org/W2071636135","https://openalex.org/W2086063785","https://openalex.org/W2088485015","https://openalex.org/W2089867244","https://openalex.org/W2093971242","https://openalex.org/W2097854981","https://openalex.org/W2133074406","https://openalex.org/W2133684960","https://openalex.org/W2139045013","https://openalex.org/W2143206135","https://openalex.org/W2170936386","https://openalex.org/W2242422039","https://openalex.org/W2313618896","https://openalex.org/W2330990923","https://openalex.org/W2463117017","https://openalex.org/W2473259021","https://openalex.org/W2558642297","https://openalex.org/W2600374250","https://openalex.org/W2608943115","https://openalex.org/W2767553047","https://openalex.org/W2795572994","https://openalex.org/W2884403958","https://openalex.org/W2909429114","https://openalex.org/W2963131515","https://openalex.org/W2976875312","https://openalex.org/W4251185801"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2793786119","https://openalex.org/W2055696851","https://openalex.org/W1967648380"],"abstract_inverted_index":{"Many":[0],"problems":[1,159],"in":[2,31,42,49,171],"nature,":[3],"being":[4],"characterized":[5],"by":[6,112],"a":[7,14,61,106,175,241],"parameter,":[8],"are":[9,29,293],"of":[10,54,63,69,85,103,126,178,275,287],"interest":[11],"both":[12,32,86],"with":[13,19,79,123],"fixed":[15],"parameter":[16,21,256,263],"value":[17],"and":[18,89,105,184,205,290],"the":[20,70,82,95,113,120,130,136,185,200,212,221,253,260,283],"approaching":[22],"an":[23,50],"asymptotic":[24],"limit.":[25],"Numerical":[26],"schemes":[27,47,147],"that":[28,198,240],"convergent":[30],"regimes":[33],"offer":[34,154],"robust":[35,155],"discretizations,":[36,183],"which":[37],"can":[38,97,246,267],"be":[39,98,248,268],"highly":[40],"desirable":[41,142],"practice.":[43],"The":[44],"asymptotically":[45,145,228],"compatible":[46,146],"studied":[48],"earlier":[51],"published":[52],"version":[53,68],"this":[55,172],"paper":[56],"meet":[57],"such":[58,149,281],"objectives":[59],"for":[60,148,199],"class":[62],"parametrized":[64,111],"problems.":[65,277],"An":[66],"extended":[67],"abstract":[71],"mathematical":[72],"framework":[73,96],"is":[74,133,141,187,226,238],"established":[75],"rigorously":[76],"here,":[77],"together":[78],"applications":[80],"to":[81,100,135,143,153,158,270],"numerical":[83,156],"solution":[84,245],"nonlocal":[87,101,127,161,201,276,288],"models":[88,102,128,150,202],"their":[90,206],"local":[91,207,243],"limits.":[92],"In":[93],"particular,":[94],"applied":[99],"diffusion":[104],"general":[107],"state-based":[108],"peridynamic":[109],"system":[110],"horizon":[114,131],"radius.":[115],"Recent":[116],"findings":[117],"have":[118],"exposed":[119],"risks":[121],"associated":[122],"some":[124],"discretizations":[125,157],"when":[129],"radius":[132],"proportional":[134],"discretization":[137,254],"parameter.":[138],"Thus,":[139],"it":[140,237],"develop":[144],"so":[151],"as":[152,209,211,250,252,282],"involving":[160],"interactions":[162],"on":[163,193],"multiple":[164],"scales.":[165],"This":[166],"work":[167],"provides":[168],"new":[169],"insight":[170],"regard":[173],"through":[174],"careful":[176],"analysis":[177],"related":[179],"conforming":[180],"finite":[181,213,223,233],"element":[182,214,224],"finding":[186],"valid":[188],"under":[189,203],"minimal":[190],"regularity":[191],"assumptions":[192],"exact":[194],"solutions.":[195],"It":[196],"reveals":[197],"consideration":[204],"limit,":[208],"long":[210,251],"space":[215],"contains":[216],"continuous":[217],"piecewise":[218,231],"linear":[219],"functions,":[220],"Galerkin":[222],"approximation":[225],"always":[227],"compatible.":[229],"For":[230],"constant":[232],"elements,":[234],"whenever":[235],"applicable,":[236],"shown":[239],"correct":[242],"limit":[244,286],"also":[247,294],"obtained":[249],"(mesh)":[255],"decreases":[257],"faster":[258],"than":[259],"modeling":[261],"(horizon)":[262],"does.":[264],"These":[265],"results":[266],"used":[269],"guide":[271],"future":[272],"computational":[273],"studies":[274],"Some":[278],"other":[279],"applications,":[280],"fractional":[284],"PDE":[285],"models,":[289],"open":[291],"questions":[292],"presented.":[295]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":5}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}
