{"id":"https://openalex.org/W2924056856","doi":"https://doi.org/10.1090/mcom/3603","title":"Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian","display_name":"Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian","publication_year":2020,"publication_date":"2020-12-02","ids":{"openalex":"https://openalex.org/W2924056856","doi":"https://doi.org/10.1090/mcom/3603","mag":"2924056856"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3603","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3603","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1903.10409","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019645947","display_name":"Markus Faustmann","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":true,"raw_author_name":"Markus Faustmann","raw_affiliation_strings":["TU Wien, Institute of Analysis und Scientific Computing, Wiedner Hauptstra\u00c3\u009fe 8-10, 1040 Wien, Austria","Vienna University of Technology"],"affiliations":[{"raw_affiliation_string":"TU Wien, Institute of Analysis und Scientific Computing, Wiedner Hauptstra\u00c3\u009fe 8-10, 1040 Wien, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Vienna University of Technology","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058356670","display_name":"Jens Markus Melenk","orcid":"https://orcid.org/0000-0001-9024-6028"},"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":"Jens Markus Melenk","raw_affiliation_strings":["TU Wien, Institute of Analysis und Scientific Computing, Wiedner Hauptstra\u00c3\u009fe 8-10, 1040 Wien, Austria","Vienna University of Technology"],"affiliations":[{"raw_affiliation_string":"TU Wien, Institute of Analysis und Scientific Computing, Wiedner Hauptstra\u00c3\u009fe 8-10, 1040 Wien, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Vienna University of Technology","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":["TU Wien, Institute of Analysis und Scientific Computing, Wiedner Hauptstra\u00c3\u009fe 8-10, 1040 Wien, Austria","Vienna University of Technology"],"affiliations":[{"raw_affiliation_string":"TU Wien, Institute of Analysis und Scientific Computing, Wiedner Hauptstra\u00c3\u009fe 8-10, 1040 Wien, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Vienna University of Technology","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5019645947"],"corresponding_institution_ids":["https://openalex.org/I145847075"],"apc_list":null,"apc_paid":null,"fwci":0.56016864,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.57716471,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"90","issue":"330","first_page":"1557","last_page":"1587"},"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":0.9991999864578247,"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"}},"topics":[{"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9987999796867371,"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"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7597591280937195},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7338085174560547},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.6581721305847168},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6017324924468994},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5631675124168396},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5349762439727783},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.515629231929779},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45832502841949463},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.45230013132095337},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.2252902388572693},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21879032254219055},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19680720567703247},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12709474563598633},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11261194944381714}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7597591280937195},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7338085174560547},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.6581721305847168},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6017324924468994},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5631675124168396},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5349762439727783},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.515629231929779},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45832502841949463},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.45230013132095337},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2252902388572693},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21879032254219055},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19680720567703247},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12709474563598633},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11261194944381714},{"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/mcom/3603","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3603","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1903.10409","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.10409","pdf_url":"https://arxiv.org/pdf/1903.10409","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":"mag:2924056856","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1903.10409","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1903.10409","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1903.10409","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1903.10409","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.10409","pdf_url":"https://arxiv.org/pdf/1903.10409","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W8052360","https://openalex.org/W986594838","https://openalex.org/W1586623601","https://openalex.org/W1602383637","https://openalex.org/W1711992483","https://openalex.org/W1965398593","https://openalex.org/W1981304176","https://openalex.org/W2009985306","https://openalex.org/W2038115135","https://openalex.org/W2039427414","https://openalex.org/W2039924562","https://openalex.org/W2044959876","https://openalex.org/W2055496542","https://openalex.org/W2072811159","https://openalex.org/W2076206883","https://openalex.org/W2084743165","https://openalex.org/W2089768471","https://openalex.org/W2092037996","https://openalex.org/W2093622765","https://openalex.org/W2097359885","https://openalex.org/W2107813568","https://openalex.org/W2291079924","https://openalex.org/W2532859297","https://openalex.org/W2740918329","https://openalex.org/W2749611175","https://openalex.org/W2756500402","https://openalex.org/W2785762403","https://openalex.org/W2887354602","https://openalex.org/W2963074984","https://openalex.org/W2963707245","https://openalex.org/W2963763304","https://openalex.org/W3021722416","https://openalex.org/W3102639848","https://openalex.org/W3103229763","https://openalex.org/W3105657163"],"related_works":["https://openalex.org/W3108519305","https://openalex.org/W2964039884","https://openalex.org/W2510312903","https://openalex.org/W2808517570","https://openalex.org/W2967662251","https://openalex.org/W2089164817","https://openalex.org/W2182570409","https://openalex.org/W3214543110","https://openalex.org/W1998985645","https://openalex.org/W2153900092","https://openalex.org/W2024669265","https://openalex.org/W102640039","https://openalex.org/W2615866843","https://openalex.org/W2473585821","https://openalex.org/W3193335938","https://openalex.org/W1982909786","https://openalex.org/W3171211115","https://openalex.org/W2081325304","https://openalex.org/W2768777660","https://openalex.org/W2538215051"],"abstract_inverted_index":{"For":[0],"the":[1,4,41,44,64,67,86,89,97],"discretization":[2],"of":[3,38,40,63,88],"integral":[5],"fractional":[6,98],"Laplacian":[7],"$(-\u0394)^s$,":[8],"$0":[9],"&lt;":[10,12,47,49],"s":[11,48],"1$,":[13,50],"based":[14],"on":[15],"piecewise":[16],"linear":[17],"functions,":[18],"we":[19],"present":[20],"and":[21],"analyze":[22],"a":[23,27,36,61],"reliable":[24],"weighted":[25,52],"residual":[26,42,53],"posteriori":[28],"error":[29,54,82],"estimator.":[30,83],"In":[31],"order":[32],"to":[33,85],"compensate":[34],"for":[35,75,96],"lack":[37],"$L^2$-regularity":[39],"in":[43],"regime":[45],"$3/4":[46],"this":[51,81],"estimator":[55],"includes":[56],"as":[57],"an":[58,76],"additional":[59],"weight":[60],"power":[62],"distance":[65],"from":[66],"mesh":[68],"skeleton.":[69],"We":[70],"prove":[71],"optimal":[72],"convergence":[73],"rates":[74],"$h$-adaptive":[77],"algorithm":[78,91],"driven":[79],"by":[80],"Key":[84],"analysis":[87],"adaptive":[90],"are":[92],"local":[93],"inverse":[94],"estimates":[95],"Laplacian.":[99]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
