{"id":"https://openalex.org/W2056598374","doi":"https://doi.org/10.1137/s0036142998349102","title":"Adaptive Galerkin Methods with Error Control for a Dynamical Ginzburg--Landau Model in Superconductivity","display_name":"Adaptive Galerkin Methods with Error Control for a Dynamical Ginzburg--Landau Model in Superconductivity","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2056598374","doi":"https://doi.org/10.1137/s0036142998349102","mag":"2056598374"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142998349102","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142998349102","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/A5100325708","display_name":"Zhiming Chen","orcid":"https://orcid.org/0000-0002-8771-4051"},"institutions":[{"id":"https://openalex.org/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhiming Chen","raw_affiliation_strings":["Institute of Computational Mathematics and Scientific/Engineering Computing of Chinese Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Institute of Computational Mathematics and Scientific/Engineering Computing of Chinese Academy of Sciences","institution_ids":["https://openalex.org/I4210090176","https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029035902","display_name":"Shibin Dai","orcid":"https://orcid.org/0000-0002-1726-4745"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shibin Dai","raw_affiliation_strings":["University of Maryland, College Park"],"affiliations":[{"raw_affiliation_string":"University of Maryland, College Park","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100325708"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210090176"],"apc_list":null,"apc_paid":null,"fwci":3.7152,"has_fulltext":false,"cited_by_count":54,"citation_normalized_percentile":{"value":0.92225714,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"38","issue":"6","first_page":"1961","last_page":"1985"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9995999932289124,"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":0.9991999864578247,"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":0.7926027178764343},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5952193737030029},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5527865290641785},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.5389633178710938},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5180373787879944},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5155158042907715},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5104071497917175},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4698186218738556},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.46003398299217224},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.44527652859687805},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.43078121542930603},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42245718836784363},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.4117385745048523},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.2895861268043518},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13610690832138062},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10558575391769409}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7926027178764343},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5952193737030029},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5527865290641785},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.5389633178710938},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5180373787879944},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5155158042907715},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5104071497917175},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4698186218738556},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.46003398299217224},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.44527652859687805},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.43078121542930603},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42245718836784363},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.4117385745048523},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2895861268043518},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13610690832138062},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10558575391769409},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0036142998349102","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142998349102","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:CiteSeerX.psu:10.1.1.138.6914","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.138.6914","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucla.edu/~sdai/paper/Chen-Dai_TDGL.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.25.4674","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.4674","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://lsec.cc.ac.cn/~zmchen/papers/tdgl.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W331840079","https://openalex.org/W1654896165","https://openalex.org/W1674659126","https://openalex.org/W1963952659","https://openalex.org/W1970850839","https://openalex.org/W1989594010","https://openalex.org/W2003378896","https://openalex.org/W2011884938","https://openalex.org/W2019658175","https://openalex.org/W2024619373","https://openalex.org/W2038626747","https://openalex.org/W2041523977","https://openalex.org/W2044749219","https://openalex.org/W2059033901","https://openalex.org/W2062279638","https://openalex.org/W2064265943","https://openalex.org/W2069048447","https://openalex.org/W2070630372","https://openalex.org/W2093518827","https://openalex.org/W2093599174","https://openalex.org/W2114567858","https://openalex.org/W2124214067","https://openalex.org/W2369386221","https://openalex.org/W4205289336","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2355560061","https://openalex.org/W1991960225","https://openalex.org/W4287752683","https://openalex.org/W2782024549","https://openalex.org/W3206471890","https://openalex.org/W2010894337","https://openalex.org/W2069123619","https://openalex.org/W2089181747","https://openalex.org/W3116159674","https://openalex.org/W2078359189"],"abstract_inverted_index":{"The":[0],"time-dependent":[1],"Ginzburg--Landau":[2],"model":[3],"which":[4,70],"describes":[5],"the":[6,43,53,56,61,72,75,78,81],"phase":[7],"transitions":[8],"taking":[9],"place":[10],"in":[11,25,28],"superconductors":[12],"is":[13,22],"a":[14,49],"coupled":[15],"system":[16],"of":[17,52,55,63,74,80],"nonlinear":[18],"parabolic":[19],"equations.":[20,65],"It":[21],"discretized":[23],"semi-implicitly":[24],"time":[26],"and":[27,77],"space":[29],"via":[30],"continuous":[31],"piecewise":[32],"linear":[33],"finite":[34],"elements.":[35],"A":[36],"posteriori":[37],"error":[38,64],"estimates":[39],"are":[40,68],"derived":[41],"for":[42],"$L^\\infty":[44],"L^2$":[45],"norm":[46],"by":[47],"studying":[48],"dual":[50,62],"problem":[51],"linearization":[54],"original":[57],"system,":[58],"other":[59],"than":[60],"Numerical":[66],"simulations":[67],"included":[69],"illustrate":[71],"reliability":[73],"estimators":[76],"flexibility":[79],"proposed":[82],"adaptive":[83],"method.":[84]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-23T09:07:50.710637","created_date":"2025-10-10T00:00:00"}
