{"id":"https://openalex.org/W2066385667","doi":"https://doi.org/10.1137/090751530","title":"Robust A Priori and A Posteriori Error Analysis for the Approximation of Allen\u2013Cahn and Ginzburg\u2013Landau Equations Past Topological Changes","display_name":"Robust A Priori and A Posteriori Error Analysis for the Approximation of Allen\u2013Cahn and Ginzburg\u2013Landau Equations Past Topological Changes","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2066385667","doi":"https://doi.org/10.1137/090751530","mag":"2066385667"},"language":"en","primary_location":{"id":"doi:10.1137/090751530","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090751530","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5017359935","display_name":"S\u00f6ren Bartels","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S\u00f6ren Bartels","raw_affiliation_strings":["bartels@ins.uni-bonn.de#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"bartels@ins.uni-bonn.de#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064048810","display_name":"R\u00fcdiger M\u00fcller","orcid":"https://orcid.org/0000-0003-2643-722X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R\u00fcdiger M\u00fcller","raw_affiliation_strings":["mueller@wias-berlin.de#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"mueller@wias-berlin.de#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061841111","display_name":"Christoph Ortner","orcid":"https://orcid.org/0000-0003-1498-8120"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christoph Ortner","raw_affiliation_strings":["ortner@maths.ox.ac.uk#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ortner@maths.ox.ac.uk#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7324,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.84361359,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"49","issue":"1","first_page":"110","last_page":"134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9979000091552734,"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/T10670","display_name":"Aluminum Alloy Microstructure Properties","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.785194993019104},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7428411245346069},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.6615588665008545},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5747057199478149},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.49199268221855164},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4456336796283722},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3354792594909668},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33148863911628723},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.32517287135124207},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28150397539138794},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11375483870506287},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07694289088249207},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07547026872634888}],"concepts":[{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.785194993019104},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7428411245346069},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.6615588665008545},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5747057199478149},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.49199268221855164},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4456336796283722},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3354792594909668},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33148863911628723},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32517287135124207},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28150397539138794},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11375483870506287},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07694289088249207},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07547026872634888},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/090751530","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090751530","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:wrap.warwick.ac.uk:43791","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","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":46,"referenced_works":["https://openalex.org/W44102725","https://openalex.org/W99776242","https://openalex.org/W272171723","https://openalex.org/W1486973064","https://openalex.org/W1493492050","https://openalex.org/W1509346826","https://openalex.org/W1539347723","https://openalex.org/W1566292686","https://openalex.org/W1966584387","https://openalex.org/W1967011851","https://openalex.org/W1969100313","https://openalex.org/W1970850839","https://openalex.org/W1971975973","https://openalex.org/W1981584551","https://openalex.org/W1982199944","https://openalex.org/W1991705702","https://openalex.org/W2018251972","https://openalex.org/W2018573482","https://openalex.org/W2019658175","https://openalex.org/W2020896229","https://openalex.org/W2023111506","https://openalex.org/W2023543626","https://openalex.org/W2026313996","https://openalex.org/W2027807211","https://openalex.org/W2030685662","https://openalex.org/W2038626747","https://openalex.org/W2040531056","https://openalex.org/W2045823559","https://openalex.org/W2047378168","https://openalex.org/W2047626766","https://openalex.org/W2053482768","https://openalex.org/W2062245988","https://openalex.org/W2069842990","https://openalex.org/W2074006304","https://openalex.org/W2079028266","https://openalex.org/W2082621526","https://openalex.org/W2088540073","https://openalex.org/W2103588786","https://openalex.org/W2115218270","https://openalex.org/W2139329469","https://openalex.org/W2169845605","https://openalex.org/W2199169705","https://openalex.org/W3148050609","https://openalex.org/W4237783740","https://openalex.org/W4256064871","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4245687327","https://openalex.org/W2112549839","https://openalex.org/W4254637135","https://openalex.org/W2905483137","https://openalex.org/W3034896902","https://openalex.org/W581800798","https://openalex.org/W3207307312","https://openalex.org/W2282634062","https://openalex.org/W4385775167","https://openalex.org/W1480770706"],"abstract_inverted_index":{"A":[0],"priori":[1],"and":[2,15,35,94,102,112],"a":[3,32,71,82],"posteriori":[4],"error":[5,84],"estimates":[6,30,41,62,79,87],"are":[7],"derived":[8],"for":[9,107],"the":[10,26,29,37,40,43,49,56,61,65,68,100,108],"numerical":[11],"approximation":[12],"of":[13,28,39,45,67,78,104,110],"scalar":[14],"complex":[16],"valued":[17],"phase":[18],"field":[19],"models.":[20],"Particular":[21],"attention":[22],"is":[23],"devoted":[24],"to":[25,36,75,90],"dependence":[27,77],"on":[31,64],"small":[33],"parameter":[34,69],"validity":[38],"in":[42,48,55,70],"presence":[44],"topological":[46,116],"changes":[47],"solution":[50],"that":[51,114],"represents":[52],"singular":[53],"points":[54],"evolution.":[57],"For":[58],"typical":[59],"singularities":[60],"depend":[63],"inverse":[66],"polynomial":[72],"as":[73],"opposed":[74],"exponential":[76],"resulting":[80],"from":[81],"straightforward":[83],"analysis.":[85],"The":[86],"naturally":[88],"lead":[89],"adaptive":[91],"mesh":[92],"refinement":[93],"coarsening":[95],"algorithms.":[96],"Numerical":[97],"experiments":[98],"illustrate":[99],"reliability":[101],"efficiency":[103],"this":[105],"approach":[106],"evolution":[109],"interfaces":[111],"vortices":[113],"undergo":[115],"changes.":[117]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
