{"id":"https://openalex.org/W1524366444","doi":"https://doi.org/10.1137/16m106073x","title":"Adaptivity and Blow-Up Detection for Nonlinear Evolution Problems","display_name":"Adaptivity and Blow-Up Detection for Nonlinear Evolution Problems","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W1524366444","doi":"https://doi.org/10.1137/16m106073x","mag":"1524366444"},"language":"en","primary_location":{"id":"doi:10.1137/16m106073x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m106073x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://discovery.dundee.ac.uk/en/publications/1ef8a13d-2354-4012-a263-c9d76c141ae4","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072274308","display_name":"Andrea Cangiani","orcid":"https://orcid.org/0000-0002-5489-2425"},"institutions":[{"id":"https://openalex.org/I153648349","display_name":"University of Leicester","ror":"https://ror.org/04h699437","country_code":"GB","type":"education","lineage":["https://openalex.org/I153648349"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Andrea Cangiani","raw_affiliation_strings":["University of Leicester"],"affiliations":[{"raw_affiliation_string":"University of Leicester","institution_ids":["https://openalex.org/I153648349"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103928074","display_name":"Emmanuil H. Georgoulis","orcid":null},"institutions":[{"id":"https://openalex.org/I153648349","display_name":"University of Leicester","ror":"https://ror.org/04h699437","country_code":"GB","type":"education","lineage":["https://openalex.org/I153648349"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Emmanuil H. Georgoulis","raw_affiliation_strings":["University of Leicester"],"affiliations":[{"raw_affiliation_string":"University of Leicester","institution_ids":["https://openalex.org/I153648349"]}]},{"author_position":"middle","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"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Irene Kyza","raw_affiliation_strings":["Department of Mathematics, University of Dundee, Nethergate, Dundee, DD1 4HN, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Dundee, Nethergate, Dundee, DD1 4HN, United Kingdom","institution_ids":["https://openalex.org/I177639307"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005503047","display_name":"Stephen Metcalfe","orcid":"https://orcid.org/0000-0002-9076-3508"},"institutions":[{"id":"https://openalex.org/I153648349","display_name":"University of Leicester","ror":"https://ror.org/04h699437","country_code":"GB","type":"education","lineage":["https://openalex.org/I153648349"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Stephen Metcalfe","raw_affiliation_strings":["University of Leicester"],"affiliations":[{"raw_affiliation_string":"University of Leicester","institution_ids":["https://openalex.org/I153648349"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5072274308"],"corresponding_institution_ids":["https://openalex.org/I153648349"],"apc_list":null,"apc_paid":null,"fwci":3.086,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.89911996,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"38","issue":"6","first_page":"A3833","last_page":"A3856"},"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":0.9988999962806702,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9987999796867371,"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":0.833594799041748},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.796170711517334},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7398461103439331},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6737853288650513},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.5999139547348022},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5940403342247009},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5650943517684937},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.52641361951828},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5012528896331787},{"id":"https://openalex.org/keywords/time-stepping","display_name":"Time stepping","score":0.4922563135623932},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4433925747871399},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4226151704788208},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.41463032364845276},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3484532833099365},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3460274934768677},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1166708767414093}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.833594799041748},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.796170711517334},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7398461103439331},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6737853288650513},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5999139547348022},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5940403342247009},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5650943517684937},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.52641361951828},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5012528896331787},{"id":"https://openalex.org/C3019693144","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Time stepping","level":3,"score":0.4922563135623932},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4433925747871399},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4226151704788208},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.41463032364845276},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3484532833099365},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3460274934768677},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1166708767414093},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/16m106073x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m106073x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:discovery.dundee.ac.uk:openaire_cris_publications/1ef8a13d-2354-4012-a263-c9d76c141ae4","is_oa":true,"landing_page_url":"https://discovery.dundee.ac.uk/en/publications/1ef8a13d-2354-4012-a263-c9d76c141ae4","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cangiani, A, Georgoulis, E H, Kyza, I & Metcalfe, S 2016, 'Adaptivity and blow-up detection for nonlinear evolution problems', SIAM Journal on Scientific Computing, vol. 38, no. 6, pp. A3833-A3856. https://doi.org/10.1137/16M106073X","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:lra.le.ac.uk:2381/40080","is_oa":true,"landing_page_url":"http://hdl.handle.net/2381/40080","pdf_url":null,"source":{"id":"https://openalex.org/S4306402365","display_name":"Leicester Research Archive (University of Leicester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I153648349","host_organization_name":"University of Leicester","host_organization_lineage":["https://openalex.org/I153648349"],"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":"Journal Article"},{"id":"pmh:oai:nottingham-repository.worktribe.com:2411738","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/2411738","pdf_url":null,"source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"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":"","raw_type":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:discovery.dundee.ac.uk:openaire_cris_publications/1ef8a13d-2354-4012-a263-c9d76c141ae4","is_oa":true,"landing_page_url":"https://discovery.dundee.ac.uk/en/publications/1ef8a13d-2354-4012-a263-c9d76c141ae4","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cangiani, A, Georgoulis, E H, Kyza, I & Metcalfe, S 2016, 'Adaptivity and blow-up detection for nonlinear evolution problems', SIAM Journal on Scientific Computing, vol. 38, no. 6, pp. A3833-A3856. https://doi.org/10.1137/16M106073X","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1959715855","display_name":"Virtual Element Method (VEM)","funder_award_id":"EP/L022745/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G639328594","display_name":null,"funder_award_id":"EP/L022745/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322644","display_name":"University of Crete","ror":"https://ror.org/00dr28g20"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320338080","display_name":"European Social Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W1498908847","https://openalex.org/W1530300983","https://openalex.org/W1545654448","https://openalex.org/W1603842336","https://openalex.org/W1964669840","https://openalex.org/W1968306057","https://openalex.org/W1977049564","https://openalex.org/W1978507854","https://openalex.org/W1982199944","https://openalex.org/W1991960225","https://openalex.org/W2006443697","https://openalex.org/W2008428857","https://openalex.org/W2009725428","https://openalex.org/W2009904819","https://openalex.org/W2022201950","https://openalex.org/W2024357442","https://openalex.org/W2026854825","https://openalex.org/W2030685662","https://openalex.org/W2034290095","https://openalex.org/W2035018155","https://openalex.org/W2037701755","https://openalex.org/W2040531056","https://openalex.org/W2041338324","https://openalex.org/W2044300169","https://openalex.org/W2047808905","https://openalex.org/W2051189027","https://openalex.org/W2055200031","https://openalex.org/W2062429788","https://openalex.org/W2067588726","https://openalex.org/W2067951086","https://openalex.org/W2073400163","https://openalex.org/W2073818494","https://openalex.org/W2074006304","https://openalex.org/W2074076510","https://openalex.org/W2088822153","https://openalex.org/W2089127417","https://openalex.org/W2099307259","https://openalex.org/W2102295719","https://openalex.org/W2137606648","https://openalex.org/W2138560307","https://openalex.org/W2147500254","https://openalex.org/W2152498898","https://openalex.org/W2152605913","https://openalex.org/W2154953812","https://openalex.org/W2169845605","https://openalex.org/W2312832458","https://openalex.org/W2595788912","https://openalex.org/W2963868392","https://openalex.org/W3101487739"],"related_works":["https://openalex.org/W2335200596","https://openalex.org/W2355560061","https://openalex.org/W2043686470","https://openalex.org/W2401732306","https://openalex.org/W4298421854","https://openalex.org/W2613898712","https://openalex.org/W2026757688","https://openalex.org/W2096756136","https://openalex.org/W2964258661","https://openalex.org/W2010894337"],"abstract_inverted_index":{"This":[0],"work":[1],"is":[2,66,86,108],"concerned":[3],"with":[4],"the":[5,42,60,63,70,82,113],"development":[6],"of":[7,59,72,81,93,116,119],"a":[8,15,17,22,35,46,90,117],"space-time":[9],"adaptive":[10,94,106],"numerical":[11],"method,":[12],"based":[13,88],"on":[14,89],"rigorous":[16],"posteriori":[18,36],"error":[19,37],"bound,":[20],"for":[21,45,97],"semilinear":[23],"convection-diffusion":[24],"problem":[25],"which":[26,123],"may":[27],"exhibit":[28,100],"blow-up":[29,114],"in":[30,41,49,56,77,84],"finite":[31,74,101],"time.":[32],"More":[33],"specifically,":[34],"bounds":[38],"are":[39],"derived":[40],"$L^{\\infty}(L^2)+L^2(H^1)$-type":[43],"norm":[44],"first":[47],"order":[48],"time":[50,85,102,115],"implicit-explicit":[51],"interior":[52],"penalty":[53],"discontinuous":[54],"Galerkin":[55],"space":[57],"discretization":[58,83],"problem,":[61],"although":[62],"theory":[64],"presented":[65],"directly":[67],"applicable":[68],"to":[69,110],"case":[71],"conforming":[73],"element":[75],"approximations":[76],"space.":[78],"The":[79,104],"choice":[80],"made":[87],"careful":[91],"analysis":[92],"time-stepping":[95],"methods":[96],"ODEs":[98],"that":[99],"blow-up.":[103,126],"new":[105],"algorithm":[107],"shown":[109],"accurately":[111],"estimate":[112],"number":[118],"problems,":[120],"including":[121],"one":[122],"exhibits":[124],"regional":[125]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}