{"id":"https://openalex.org/W2236322917","doi":"https://doi.org/10.1007/s00211-016-0836-8","title":"Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations","display_name":"Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations","publication_year":2016,"publication_date":"2016-08-11","ids":{"openalex":"https://openalex.org/W2236322917","doi":"https://doi.org/10.1007/s00211-016-0836-8","mag":"2236322917","pmid":"https://pubmed.ncbi.nlm.nih.gov/28615749"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-016-0836-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-016-0836-8","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00211-016-0836-8.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs00211-016-0836-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035803720","display_name":"Michael Feischl","orcid":"https://orcid.org/0000-0001-7206-1652"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Michael Feischl","raw_affiliation_strings":["The Red Centre, School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052 Australia","The Red Centre, School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Red Centre, School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052 Australia","institution_ids":[]},{"raw_affiliation_string":"The Red Centre, School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055151843","display_name":"Gregor Gantner","orcid":"https://orcid.org/0000-0002-0324-5674"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Gregor Gantner","raw_affiliation_strings":["Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstra\u00dfe 8-10, 1040 Vienna, Austria","Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstra\u00dfe 8-10, 1040, Vienna, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstra\u00dfe 8-10, 1040 Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstra\u00dfe 8-10, 1040, Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089625006","display_name":"Alexander Haberl","orcid":null},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Alexander Haberl","raw_affiliation_strings":["Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstra\u00dfe 8-10, 1040 Vienna, Austria","Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstra\u00dfe 8-10, 1040, Vienna, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstra\u00dfe 8-10, 1040 Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstra\u00dfe 8-10, 1040, Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022125095","display_name":"Dirk Praetorius","orcid":"https://orcid.org/0000-0002-1977-9830"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Dirk Praetorius","raw_affiliation_strings":["Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstra\u00dfe 8-10, 1040 Vienna, Austria","Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstra\u00dfe 8-10, 1040, Vienna, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstra\u00dfe 8-10, 1040 Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstra\u00dfe 8-10, 1040, Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5055151843"],"corresponding_institution_ids":["https://openalex.org/I145847075"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":3.7055,"has_fulltext":true,"cited_by_count":23,"citation_normalized_percentile":{"value":0.9216823,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"136","issue":"1","first_page":"147","last_page":"182"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","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/T11245","display_name":"Advanced Numerical Analysis Techniques","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/T10514","display_name":"Numerical methods in engineering","score":0.9887999892234802,"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":0.9829999804496765,"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":0.8667981624603271},{"id":"https://openalex.org/keywords/isogeometric-analysis","display_name":"Isogeometric analysis","score":0.6646859049797058},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5529303550720215},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5045422315597534},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.48802104592323303},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4825141131877899},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.45020121335983276},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.43344298005104065},{"id":"https://openalex.org/keywords/adaptive-mesh-refinement","display_name":"Adaptive mesh refinement","score":0.42447909712791443},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41949188709259033},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1849852204322815}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8667981624603271},{"id":"https://openalex.org/C2780737243","wikidata":"https://www.wikidata.org/wiki/Q17082433","display_name":"Isogeometric analysis","level":3,"score":0.6646859049797058},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5529303550720215},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5045422315597534},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.48802104592323303},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4825141131877899},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.45020121335983276},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.43344298005104065},{"id":"https://openalex.org/C131053463","wikidata":"https://www.wikidata.org/wiki/Q4680751","display_name":"Adaptive mesh refinement","level":2,"score":0.42447909712791443},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41949188709259033},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1849852204322815},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s00211-016-0836-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-016-0836-8","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00211-016-0836-8.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmid:28615749","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28615749","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische mathematik","raw_type":null},{"id":"pmh:oai:arXiv.org:1510.05111","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1510.05111","pdf_url":"https://arxiv.org/pdf/1510.05111","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:europepmc.org:4316946","is_oa":true,"landing_page_url":"http://europepmc.org/articles/PMC5445587","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"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":"","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:5445587","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5445587","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Numer Math (Heidelb)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s00211-016-0836-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-016-0836-8","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00211-016-0836-8.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1742109135","display_name":"Dissipation and dispersion in differential equations","funder_award_id":"W1245","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3445509017","display_name":"Novel Approaches for Problems with Uncertainties","funder_award_id":"DP160101755","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G5394959934","display_name":"Optimal adaptivity for BEM and FEM-BEM coupling","funder_award_id":"P27005","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G737578855","display_name":"Optimal isogeometric boundary element methods","funder_award_id":"P29096","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320322839","display_name":"Technische Universit\u00e4t Wien","ror":"https://ror.org/04d836q62"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2236322917.pdf","grobid_xml":"https://content.openalex.org/works/W2236322917.grobid-xml"},"referenced_works_count":50,"referenced_works":["https://openalex.org/W8052360","https://openalex.org/W168205200","https://openalex.org/W642107583","https://openalex.org/W1510620315","https://openalex.org/W1602383637","https://openalex.org/W1711992483","https://openalex.org/W1914905521","https://openalex.org/W1964475218","https://openalex.org/W1965398593","https://openalex.org/W1973737329","https://openalex.org/W1974033468","https://openalex.org/W1983457966","https://openalex.org/W1986120564","https://openalex.org/W1990254060","https://openalex.org/W1991670087","https://openalex.org/W2000425991","https://openalex.org/W2001440251","https://openalex.org/W2003277202","https://openalex.org/W2038115135","https://openalex.org/W2039924562","https://openalex.org/W2044947739","https://openalex.org/W2050871234","https://openalex.org/W2053620226","https://openalex.org/W2055496542","https://openalex.org/W2061960130","https://openalex.org/W2074623661","https://openalex.org/W2075720940","https://openalex.org/W2076945160","https://openalex.org/W2082092602","https://openalex.org/W2092037996","https://openalex.org/W2097359885","https://openalex.org/W2106678274","https://openalex.org/W2107813568","https://openalex.org/W2129372062","https://openalex.org/W2131933182","https://openalex.org/W2134169343","https://openalex.org/W2137757379","https://openalex.org/W2144098834","https://openalex.org/W2168133360","https://openalex.org/W2172294702","https://openalex.org/W2206115491","https://openalex.org/W2396668358","https://openalex.org/W2496081756","https://openalex.org/W2963066470","https://openalex.org/W2963675990","https://openalex.org/W3101546251","https://openalex.org/W3122997955","https://openalex.org/W4237713727","https://openalex.org/W4292079583","https://openalex.org/W4293238311"],"related_works":["https://openalex.org/W1940709639","https://openalex.org/W1924025565","https://openalex.org/W3025313650","https://openalex.org/W4297362898","https://openalex.org/W2352095914","https://openalex.org/W2989766329","https://openalex.org/W2129372062","https://openalex.org/W2981315515","https://openalex.org/W2615762530","https://openalex.org/W2554232049"],"abstract_inverted_index":{"In":[0,49],"a":[1,16,55,72],"recent":[2],"work":[3],"(Feischl":[4],"et":[5],"al.":[6],"in":[7,25,89],"Eng":[8],"Anal":[9],"Bound":[10],"Elem":[11],"62:141-153,":[12],"2016),":[13],"we":[14,53],"analyzed":[15],"weighted-residual":[17],"error":[18],"estimator":[19],"for":[20,87],"isogeometric":[21],"boundary":[22],"element":[23],"methods":[24],"2D":[26],"and":[27],"proposed":[28],"an":[29],"adaptive":[30],"algorithm":[31,60],"which":[32,76],"steers":[33],"the":[34,38,44,47,50,79],"local":[35],"mesh-refinement":[36],"of":[37,46],"underlying":[39],"partition":[40],"as":[41,43,82,84],"well":[42,83],"multiplicity":[45,81],"knots.":[48],"present":[51],"work,":[52],"give":[54],"mathematical":[56],"proof":[57],"that":[58],"this":[59],"leads":[61],"to":[62],"convergence":[63],"even":[64],"with":[65],"optimal":[66],"algebraic":[67],"rates.":[68],"Technical":[69],"contributions":[70],"include":[71],"novel":[73],"mesh-size":[74],"function":[75],"also":[77],"monitors":[78],"knot":[80],"inverse":[85],"estimates":[86],"NURBS":[88],"fractional-order":[90],"Sobolev":[91],"norms.":[92]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}