{"id":"https://openalex.org/W2995818232","doi":"https://doi.org/10.1080/00207160.2019.1706729","title":"Superconvergence analysis for a nonlinear parabolic equation with a BDF finite element method","display_name":"Superconvergence analysis for a nonlinear parabolic equation with a BDF finite element method","publication_year":2019,"publication_date":"2019-12-18","ids":{"openalex":"https://openalex.org/W2995818232","doi":"https://doi.org/10.1080/00207160.2019.1706729","mag":"2995818232"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2019.1706729","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2019.1706729","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5100607462","display_name":"Junjun Wang","orcid":"https://orcid.org/0000-0002-4669-8657"},"institutions":[{"id":"https://openalex.org/I151878197","display_name":"Pingdingshan University","ror":"https://ror.org/026c29h90","country_code":"CN","type":"education","lineage":["https://openalex.org/I151878197"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Junjun Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Pingdingshan University, Pingdingshan, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Pingdingshan University, Pingdingshan, People's Republic of China","institution_ids":["https://openalex.org/I151878197"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100898677","display_name":"Xiaoxia Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I151878197","display_name":"Pingdingshan University","ror":"https://ror.org/026c29h90","country_code":"CN","type":"education","lineage":["https://openalex.org/I151878197"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoxia Yang","raw_affiliation_strings":["School of Mathematics and Statistics, Pingdingshan University, Pingdingshan, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Pingdingshan University, Pingdingshan, People's Republic of China","institution_ids":["https://openalex.org/I151878197"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100607462"],"corresponding_institution_ids":["https://openalex.org/I151878197"],"apc_list":null,"apc_paid":null,"fwci":0.5606,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.65950864,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"97","issue":"12","first_page":"2487","last_page":"2506"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9980999827384949,"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/T10514","display_name":"Numerical methods in engineering","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/superconvergence","display_name":"Superconvergence","score":0.9615987539291382},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.858924388885498},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6923559904098511},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6872250437736511},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.5903175473213196},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5727425813674927},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5636789202690125},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5194939374923706},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5185347199440002},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.5064009428024292},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.488352507352829},{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.4375225901603699},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4027421474456787}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.9615987539291382},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.858924388885498},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6923559904098511},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6872250437736511},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5903175473213196},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5727425813674927},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5636789202690125},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5194939374923706},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5185347199440002},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.5064009428024292},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.488352507352829},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.4375225901603699},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4027421474456787},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2019.1706729","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2019.1706729","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6735760241","display_name":"\u975e\u7ebf\u6027\u53d1\u5c55\u65b9\u7a0b\u7684\u5404\u5411\u5f02\u6027\u9ad8\u7cbe\u5ea6\u65e0\u7f51\u683c\u6bd4\u6709\u9650\u5143\u65b9\u6cd5\u65b0\u6a21\u5f0f\u7814\u7a76","funder_award_id":"11671369","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W99776242","https://openalex.org/W213073004","https://openalex.org/W1975176010","https://openalex.org/W1988386904","https://openalex.org/W2004017120","https://openalex.org/W2008947598","https://openalex.org/W2027822086","https://openalex.org/W2039046333","https://openalex.org/W2046883902","https://openalex.org/W2061401303","https://openalex.org/W2067889604","https://openalex.org/W2121410213","https://openalex.org/W2157121421","https://openalex.org/W2165807641","https://openalex.org/W2319973481","https://openalex.org/W2467378457","https://openalex.org/W2526613690","https://openalex.org/W2759992807","https://openalex.org/W2888626034"],"related_works":["https://openalex.org/W2019032602","https://openalex.org/W4318305492","https://openalex.org/W4389778560","https://openalex.org/W3199641408","https://openalex.org/W2597229022","https://openalex.org/W2947552135","https://openalex.org/W2014920306","https://openalex.org/W2984453791","https://openalex.org/W1982175859","https://openalex.org/W2508014856"],"abstract_inverted_index":{"Superconvergence":[0],"analysis":[1],"for":[2],"a":[3,10,38],"nonlinear":[4],"parabolic":[5],"equation":[6],"is":[7,32,92,106],"studied":[8],"with":[9,47,53,89],"linearized":[11],"2-step":[12],"backward":[13],"differential":[14],"formula":[15],"(BDF)":[16],"Galerkin":[17],"finite":[18],"element":[19],"method":[20],"(FEM).":[21],"The":[22,41,59],"error":[23,43,61],"between":[24],"the":[25,29,67,72,81,98,101,107],"exact":[26],"solution":[27,31,74],"and":[28,50,66,110],"numerical":[30,73,95],"split":[33],"into":[34],"two":[35],"parts":[36],"by":[37],"time-discrete":[39],"system.":[40],"temporal":[42],"estimates":[44,62],"in":[45,51,75,87],"H1-norm":[46,88],"order":[48,54,90],"O(\u03c42)":[49],"H2-norm":[52],"O(\u03c43/2)":[55],"are":[56,63],"derived,":[57],"respectively.":[58],"spatial":[60],"deduced":[64],"unconditionally":[65],"results":[68],"help":[69],"to":[70],"bound":[71],"L\u221e-norm.":[76],"By":[77],"some":[78],"new":[79],"way,":[80],"unconditional":[82],"superclose":[83],"property":[84],"of":[85,100],"un":[86],"O(h2+\u03c42)":[91],"obtained.":[93],"Two":[94],"examples":[96],"show":[97],"validity":[99],"theoretical":[102],"analysis.":[103],"Here,":[104],"h":[105],"subdivision":[108],"parameter,":[109],"\u03c4,":[111],"time":[112],"step":[113],"size.":[114]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
