{"id":"https://openalex.org/W1971039174","doi":"https://doi.org/10.1007/s00211-014-0634-0","title":"A posteriori error control and adaptivity for Crank\u2013Nicolson finite element approximations for the linear Schr\u00f6dinger equation","display_name":"A posteriori error control and adaptivity for Crank\u2013Nicolson finite element approximations for the linear Schr\u00f6dinger equation","publication_year":2014,"publication_date":"2014-05-08","ids":{"openalex":"https://openalex.org/W1971039174","doi":"https://doi.org/10.1007/s00211-014-0634-0","mag":"1971039174"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-014-0634-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-014-0634-0","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","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/A5045046421","display_name":"Theodoros Katsaounis","orcid":"https://orcid.org/0000-0001-7387-7987"},"institutions":[{"id":"https://openalex.org/I142617266","display_name":"University of Crete","ror":"https://ror.org/00dr28g20","country_code":"GR","type":"education","lineage":["https://openalex.org/I142617266"]},{"id":"https://openalex.org/I8901234","display_name":"Foundation for Research and Technology Hellas","ror":"https://ror.org/052rphn09","country_code":"GR","type":"facility","lineage":["https://openalex.org/I8901234"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Theodoros Katsaounis","raw_affiliation_strings":["Department of Mathematics and Applied Mathematics, University of Crete, 71409 , Heraklion-Crete, Greece","Institute of Applied and Computational Mathematics, Foundation of Research and Technology-Hellas, Nikolaou Plastira 100, Vassilika Vouton, 700 13, , Heraklion-Crete, Greece","Department of Mathematics and Applied Mathematics, University of Crete, 71409\u00a0, Heraklion-Crete, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, University of Crete, 71409 , Heraklion-Crete, Greece","institution_ids":["https://openalex.org/I142617266"]},{"raw_affiliation_string":"Institute of Applied and Computational Mathematics, Foundation of Research and Technology-Hellas, Nikolaou Plastira 100, Vassilika Vouton, 700 13, , Heraklion-Crete, Greece","institution_ids":["https://openalex.org/I8901234"]},{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, University of Crete, 71409\u00a0, Heraklion-Crete, Greece","institution_ids":["https://openalex.org/I142617266"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080449023","display_name":"Irene Kyza","orcid":"https://orcid.org/0000-0003-1749-9517"},"institutions":[{"id":"https://openalex.org/I177639307","display_name":"University of Dundee","ror":"https://ror.org/03h2bxq36","country_code":"GB","type":"education","lineage":["https://openalex.org/I177639307"]},{"id":"https://openalex.org/I8901234","display_name":"Foundation for Research and Technology Hellas","ror":"https://ror.org/052rphn09","country_code":"GR","type":"facility","lineage":["https://openalex.org/I8901234"]}],"countries":["GB","GR"],"is_corresponding":true,"raw_author_name":"Irene Kyza","raw_affiliation_strings":["Division of Mathematics, University of Dundee, Dundee, DD1 4HN, Scotland, UK","Institute of Applied and Computational Mathematics, Foundation of Research and Technology-Hellas, Nikolaou Plastira 100, Vassilika Vouton, 700 13, , Heraklion-Crete, Greece","Institute of Applied and Computational Mathematics, Foundation of Research and Technology-Hellas, Nikolaou Plastira 100, Vassilika Vouton, 700 13,\u00a0, Heraklion-Crete, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Mathematics, University of Dundee, Dundee, DD1 4HN, Scotland, UK","institution_ids":["https://openalex.org/I177639307"]},{"raw_affiliation_string":"Institute of Applied and Computational Mathematics, Foundation of Research and Technology-Hellas, Nikolaou Plastira 100, Vassilika Vouton, 700 13, , Heraklion-Crete, Greece","institution_ids":["https://openalex.org/I8901234"]},{"raw_affiliation_string":"Institute of Applied and Computational Mathematics, Foundation of Research and Technology-Hellas, Nikolaou Plastira 100, Vassilika Vouton, 700 13,\u00a0, Heraklion-Crete, Greece","institution_ids":["https://openalex.org/I8901234"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080449023"],"corresponding_institution_ids":["https://openalex.org/I177639307","https://openalex.org/I8901234"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.288,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.77671467,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"129","issue":"1","first_page":"55","last_page":"90"},"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":0.9990000128746033,"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":0.9990000128746033,"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":0.9958000183105469,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9954000115394592,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7955203652381897},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7437111139297485},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6389738917350769},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5629500150680542},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5516300797462463},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5294318199157715},{"id":"https://openalex.org/keywords/semiclassical-physics","display_name":"Semiclassical physics","score":0.5237584114074707},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.4791654646396637},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.4757213890552521},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4701295793056488},{"id":"https://openalex.org/keywords/crank\u2013nicolson-method","display_name":"Crank\u2013Nicolson method","score":0.46875882148742676},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34350883960723877},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.15533319115638733},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09243738651275635}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7955203652381897},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7437111139297485},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6389738917350769},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5629500150680542},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5516300797462463},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5294318199157715},{"id":"https://openalex.org/C535169671","wikidata":"https://www.wikidata.org/wiki/Q17080006","display_name":"Semiclassical physics","level":3,"score":0.5237584114074707},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.4791654646396637},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4757213890552521},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4701295793056488},{"id":"https://openalex.org/C180931078","wikidata":"https://www.wikidata.org/wiki/Q588725","display_name":"Crank\u2013Nicolson method","level":3,"score":0.46875882148742676},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34350883960723877},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.15533319115638733},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09243738651275635},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00211-014-0634-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-014-0634-0","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:discovery.dundee.ac.uk:openaire_cris_publications/a032fa21-a217-4450-ba23-2b156292f9bf","is_oa":false,"landing_page_url":"https://discovery.dundee.ac.uk/en/publications/a032fa21-a217-4450-ba23-2b156292f9bf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400523","display_name":"Discovery Research Portal (University of Dundee)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177639307","host_organization_name":"University of Dundee","host_organization_lineage":["https://openalex.org/I177639307"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Katsaounis, T & Kyza, I 2015, 'A posteriori error control and adaptivity for Crank-Nicolson finite element approximations for the linear Schr\u00f6dinger equation', Numerische Mathematik, vol. 129, no. 1, pp. 55-90. https://doi.org/10.1007/s00211-014-0634-0","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W24460554","https://openalex.org/W100357283","https://openalex.org/W126152219","https://openalex.org/W1488071155","https://openalex.org/W1491636742","https://openalex.org/W1492326914","https://openalex.org/W1915508819","https://openalex.org/W1965767361","https://openalex.org/W1973664641","https://openalex.org/W1983797262","https://openalex.org/W2009985306","https://openalex.org/W2013529907","https://openalex.org/W2016903605","https://openalex.org/W2022298431","https://openalex.org/W2022936648","https://openalex.org/W2025163266","https://openalex.org/W2028967809","https://openalex.org/W2030685662","https://openalex.org/W2032222091","https://openalex.org/W2047133076","https://openalex.org/W2051952162","https://openalex.org/W2052589794","https://openalex.org/W2056467685","https://openalex.org/W2056971052","https://openalex.org/W2064265943","https://openalex.org/W2074006304","https://openalex.org/W2074306248","https://openalex.org/W2084977619","https://openalex.org/W2088552913","https://openalex.org/W2099662641","https://openalex.org/W2162870748","https://openalex.org/W2199169705","https://openalex.org/W2312832458","https://openalex.org/W2318325762","https://openalex.org/W2331190391","https://openalex.org/W2591048038","https://openalex.org/W3042562017","https://openalex.org/W4242935407"],"related_works":["https://openalex.org/W3018725393","https://openalex.org/W4287813962","https://openalex.org/W2034836031","https://openalex.org/W2017697891","https://openalex.org/W1964726280","https://openalex.org/W1979610302","https://openalex.org/W2349531595","https://openalex.org/W2294059517","https://openalex.org/W2101135948","https://openalex.org/W4327854104"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-10-10T00:00:00"}
