{"id":"https://openalex.org/W2954509393","doi":"https://doi.org/10.1515/cmam-2018-0207","title":"Alternative Enriched Test Spaces in the DPG Method for Singular Perturbation Problems","display_name":"Alternative Enriched Test Spaces in the DPG Method for Singular Perturbation Problems","publication_year":2019,"publication_date":"2019-04-11","ids":{"openalex":"https://openalex.org/W2954509393","doi":"https://doi.org/10.1515/cmam-2018-0207","mag":"2954509393"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2018-0207","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0207","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","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/A5007511412","display_name":"Jacob Salazar","orcid":null},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jacob Salazar","raw_affiliation_strings":["Institute for Computational Engineering and Sciences (ICES) , The University of Texas at Austin , 2 01 E 24th St , Austin , TX 78712 , USA"],"affiliations":[{"raw_affiliation_string":"Institute for Computational Engineering and Sciences (ICES) , The University of Texas at Austin , 2 01 E 24th St , Austin , TX 78712 , USA","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059144735","display_name":"Jaime Mora","orcid":null},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jaime Mora","raw_affiliation_strings":["Institute for Computational Engineering and Sciences (ICES) , The University of Texas at Austin , 2 01 E 24th St , Austin , TX 78712 , USA"],"affiliations":[{"raw_affiliation_string":"Institute for Computational Engineering and Sciences (ICES) , The University of Texas at Austin , 2 01 E 24th St , Austin , TX 78712 , USA","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082045365","display_name":"Leszek Demkowicz","orcid":"https://orcid.org/0000-0001-7839-8037"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Leszek Demkowicz","raw_affiliation_strings":["Institute for Computational Engineering and Sciences (ICES) , The University of Texas at Austin , 2 01 E 24th St , Austin , TX 78712 , USA"],"affiliations":[{"raw_affiliation_string":"Institute for Computational Engineering and Sciences (ICES) , The University of Texas at Austin , 2 01 E 24th St , Austin , TX 78712 , USA","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5007511412"],"corresponding_institution_ids":["https://openalex.org/I86519309"],"apc_list":null,"apc_paid":null,"fwci":1.5133,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.8095068,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"19","issue":"3","first_page":"603","last_page":"630"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9997000098228455,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9994000196456909,"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":0.7141779661178589},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5659339427947998},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5409579873085022},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49321049451828003},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4325867295265198},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35805797576904297},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2958422601222992}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7141779661178589},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5659339427947998},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5409579873085022},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49321049451828003},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4325867295265198},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35805797576904297},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2958422601222992},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2018-0207","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0207","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W35607977","https://openalex.org/W181225834","https://openalex.org/W642107583","https://openalex.org/W1673768543","https://openalex.org/W1955273710","https://openalex.org/W1975941099","https://openalex.org/W1987535721","https://openalex.org/W2028246274","https://openalex.org/W2048846455","https://openalex.org/W2060065779","https://openalex.org/W2071338681","https://openalex.org/W2075865464","https://openalex.org/W2092081569","https://openalex.org/W2158928686","https://openalex.org/W2249807645","https://openalex.org/W2495211843","https://openalex.org/W4237713727","https://openalex.org/W4239704419"],"related_works":["https://openalex.org/W2066091055","https://openalex.org/W2040186499","https://openalex.org/W4377003522","https://openalex.org/W4249580765","https://openalex.org/W2096753949","https://openalex.org/W2990473846","https://openalex.org/W1985218657","https://openalex.org/W1557945163","https://openalex.org/W2742285599","https://openalex.org/W2064847051"],"abstract_inverted_index":{"Abstract":[0],"We":[1,210],"propose":[2,160],"and":[3,78,216,225],"investigate":[4],"the":[5,13,45,65,90,118,131,135,141,155,163,172,198],"application":[6],"of":[7,56,200,206],"alternative":[8],"enriched":[9],"test":[10,84,112,120,137,151,157,165,202,208],"spaces":[11,166,181,203],"in":[12,69,75,140],"discontinuous":[14],"Petrov\u2013Galerkin":[15],"(DPG)":[16],"finite":[17],"element":[18],"framework":[19],"for":[20,44,53,64,110,154],"singular":[21],"perturbation":[22,173],"linear":[23],"problems,":[24,57],"with":[25,167,179,204,228],"an":[26,184],"emphasis":[27],"on":[28,171,183],"2D":[29],"convection-dominated":[30],"diffusion.":[31],"Providing":[32],"robust":[33],"<m:math":[34,92],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[35,93],"<m:msup>":[36,94],"<m:mi>L</m:mi>":[37,95],"<m:mn>2</m:mn>":[38,96],"</m:msup>":[39,97],"</m:math>":[40,98],"{L^{2}}":[41,99],"error":[42],"estimates":[43],"field":[46],"variables":[47],"is":[48],"considered":[49],"a":[50,213,217],"convenient":[51],"feature":[52],"this":[54,59,73,146],"class":[55],"since":[58],"norm":[60,121,215],"would":[61],"not":[62],"account":[63],"large":[66],"gradients":[67],"present":[68],"boundary":[70],"layers.":[71],"With":[72],"requirement":[74],"mind,":[76],"Demkowicz":[77],"others":[79],"have":[80],"previously":[81],"formulated":[82],"special":[83],"norms,":[85],"which":[86,114],"through":[87,107],"DPG":[88,142],"deliver":[89],"desired":[91],"convergence.":[100],"However,":[101],"robustness":[102],"has":[103,125],"only":[104],"been":[105],"verified":[106],"numerical":[108],"experiments":[109],"tailored":[111],"norms":[113],"are":[115,190],"problem-specific,":[116],"whereas":[117],"quasi-optimal":[119,156],"(not":[122],"problem":[123],"specific)":[124],"failed":[126],"such":[127],"tests":[128],"due":[129],"to":[130,133,161,196,221],"difficulty":[132],"resolve":[134],"optimal":[136,150],"functions":[138,152,168],"sought":[139],"technology.":[143],"To":[144],"address":[145],"issue":[147],"(i.e.":[148],"improve":[149,222],"resolution":[153],"norm),":[158],"we":[159,177],"discretize":[162],"local":[164],"that":[169,205],"depend":[170],"parameter":[174],"\u03f5.":[175],"Explicitly,":[176],"work":[178],"B-spline":[180],"defined":[182],"\u03f5-dependent":[185],"Shishkin":[186],"submesh.":[187],"Two":[188],"examples":[189],"run":[191],"using":[192],"adaptive":[193],"h":[194],"-refinement":[195],"compare":[197],"performance":[199,224],"proposed":[201],"standard":[207],"spaces.":[209],"also":[211],"include":[212],"modified":[214],"continuation":[218],"strategy":[219],"aiming":[220],"time":[223],"briefly":[226],"experiment":[227],"these":[229],"ideas.":[230]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}