{"id":"https://openalex.org/W3190956650","doi":"https://doi.org/10.1007/s10915-021-01587-9","title":"Error Estimates of a Continuous Galerkin Time Stepping Method for Subdiffusion Problem","display_name":"Error Estimates of a Continuous Galerkin Time Stepping Method for Subdiffusion Problem","publication_year":2021,"publication_date":"2021-07-29","ids":{"openalex":"https://openalex.org/W3190956650","doi":"https://doi.org/10.1007/s10915-021-01587-9","mag":"3190956650"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-021-01587-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-021-01587-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01587-9.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01587-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052589618","display_name":"Yuyuan Yan","orcid":null},"institutions":[{"id":"https://openalex.org/I137265193","display_name":"University of Chester","ror":"https://ror.org/01drpwb22","country_code":"GB","type":"education","lineage":["https://openalex.org/I137265193"]},{"id":"https://openalex.org/I161346416","display_name":"Jimei University","ror":"https://ror.org/03hknyb50","country_code":"CN","type":"education","lineage":["https://openalex.org/I161346416"]},{"id":"https://openalex.org/I4210113003","display_name":"Physical Sciences (United States)","ror":"https://ror.org/021qvjc46","country_code":"US","type":"company","lineage":["https://openalex.org/I4210113003"]}],"countries":["CN","GB","US"],"is_corresponding":true,"raw_author_name":"Yuyuan Yan","raw_affiliation_strings":["Department of Mathematical and Physical Sciences, University of Chester, CH1 4BJ, Chester, England","School of Sciences, Jimei University, Xiamen, 361021, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical and Physical Sciences, University of Chester, CH1 4BJ, Chester, England","institution_ids":["https://openalex.org/I137265193","https://openalex.org/I4210113003"]},{"raw_affiliation_string":"School of Sciences, Jimei University, Xiamen, 361021, China","institution_ids":["https://openalex.org/I161346416"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Yuyuan Yan","orcid":null},"institutions":[{"id":"https://openalex.org/I137265193","display_name":"University of Chester","ror":"https://ror.org/01drpwb22","country_code":"GB","type":"education","lineage":["https://openalex.org/I137265193"]},{"id":"https://openalex.org/I161346416","display_name":"Jimei University","ror":"https://ror.org/03hknyb50","country_code":"CN","type":"education","lineage":["https://openalex.org/I161346416"]},{"id":"https://openalex.org/I4210113003","display_name":"Physical Sciences (United States)","ror":"https://ror.org/021qvjc46","country_code":"US","type":"company","lineage":["https://openalex.org/I4210113003"]}],"countries":["CN","GB","US"],"is_corresponding":false,"raw_author_name":"Yuyuan Yan","raw_affiliation_strings":["Department of Mathematical and Physical Sciences, University of Chester, CH1 4BJ, Chester, England","School of Sciences, Jimei University, Xiamen, 361021, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical and Physical Sciences, University of Chester, CH1 4BJ, Chester, England","institution_ids":["https://openalex.org/I137265193","https://openalex.org/I4210113003"]},{"raw_affiliation_string":"School of Sciences, Jimei University, Xiamen, 361021, China","institution_ids":["https://openalex.org/I161346416"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029448672","display_name":"Bernard A. Egwu","orcid":null},"institutions":[{"id":"https://openalex.org/I137265193","display_name":"University of Chester","ror":"https://ror.org/01drpwb22","country_code":"GB","type":"education","lineage":["https://openalex.org/I137265193"]},{"id":"https://openalex.org/I161346416","display_name":"Jimei University","ror":"https://ror.org/03hknyb50","country_code":"CN","type":"education","lineage":["https://openalex.org/I161346416"]},{"id":"https://openalex.org/I4210113003","display_name":"Physical Sciences (United States)","ror":"https://ror.org/021qvjc46","country_code":"US","type":"company","lineage":["https://openalex.org/I4210113003"]}],"countries":["CN","GB","US"],"is_corresponding":false,"raw_author_name":"Bernard A. Egwu","raw_affiliation_strings":["Department of Mathematical and Physical Sciences, University of Chester, CH1 4BJ, Chester, England","School of Sciences, Jimei University, Xiamen, 361021, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical and Physical Sciences, University of Chester, CH1 4BJ, Chester, England","institution_ids":["https://openalex.org/I137265193","https://openalex.org/I4210113003"]},{"raw_affiliation_string":"School of Sciences, Jimei University, Xiamen, 361021, China","institution_ids":["https://openalex.org/I161346416"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100712902","display_name":"Zongqi Liang","orcid":"https://orcid.org/0000-0001-8755-7837"},"institutions":[{"id":"https://openalex.org/I137265193","display_name":"University of Chester","ror":"https://ror.org/01drpwb22","country_code":"GB","type":"education","lineage":["https://openalex.org/I137265193"]},{"id":"https://openalex.org/I161346416","display_name":"Jimei University","ror":"https://ror.org/03hknyb50","country_code":"CN","type":"education","lineage":["https://openalex.org/I161346416"]},{"id":"https://openalex.org/I4210113003","display_name":"Physical Sciences (United States)","ror":"https://ror.org/021qvjc46","country_code":"US","type":"company","lineage":["https://openalex.org/I4210113003"]}],"countries":["CN","GB","US"],"is_corresponding":false,"raw_author_name":"Zongqi Liang","raw_affiliation_strings":["School of Sciences, Jimei University, Xiamen, 361021, China","Department of Mathematical and Physical Sciences, University of Chester, CH1 4BJ, Chester, England"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Sciences, Jimei University, Xiamen, 361021, China","institution_ids":["https://openalex.org/I161346416"]},{"raw_affiliation_string":"Department of Mathematical and Physical Sciences, University of Chester, CH1 4BJ, Chester, England","institution_ids":["https://openalex.org/I137265193","https://openalex.org/I4210113003"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003578513","display_name":"Yubin Yan","orcid":"https://orcid.org/0000-0002-5686-5017"},"institutions":[{"id":"https://openalex.org/I137265193","display_name":"University of Chester","ror":"https://ror.org/01drpwb22","country_code":"GB","type":"education","lineage":["https://openalex.org/I137265193"]},{"id":"https://openalex.org/I161346416","display_name":"Jimei University","ror":"https://ror.org/03hknyb50","country_code":"CN","type":"education","lineage":["https://openalex.org/I161346416"]},{"id":"https://openalex.org/I4210113003","display_name":"Physical Sciences (United States)","ror":"https://ror.org/021qvjc46","country_code":"US","type":"company","lineage":["https://openalex.org/I4210113003"]}],"countries":["CN","GB","US"],"is_corresponding":true,"raw_author_name":"Yubin Yan","raw_affiliation_strings":["Department of Mathematical and Physical Sciences, University of Chester, CH1 4BJ, Chester, England","School of Sciences, Jimei University, Xiamen, 361021, China"],"raw_orcid":"https://orcid.org/0000-0002-5686-5017","affiliations":[{"raw_affiliation_string":"Department of Mathematical and Physical Sciences, University of Chester, CH1 4BJ, Chester, England","institution_ids":["https://openalex.org/I137265193","https://openalex.org/I4210113003"]},{"raw_affiliation_string":"School of Sciences, Jimei University, Xiamen, 361021, China","institution_ids":["https://openalex.org/I161346416"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003578513","display_name":"Yubin Yan","orcid":"https://orcid.org/0000-0002-5686-5017"},"institutions":[{"id":"https://openalex.org/I137265193","display_name":"University of Chester","ror":"https://ror.org/01drpwb22","country_code":"GB","type":"education","lineage":["https://openalex.org/I137265193"]},{"id":"https://openalex.org/I161346416","display_name":"Jimei University","ror":"https://ror.org/03hknyb50","country_code":"CN","type":"education","lineage":["https://openalex.org/I161346416"]},{"id":"https://openalex.org/I4210113003","display_name":"Physical Sciences (United States)","ror":"https://ror.org/021qvjc46","country_code":"US","type":"company","lineage":["https://openalex.org/I4210113003"]}],"countries":["CN","GB","US"],"is_corresponding":false,"raw_author_name":"Yubin Yan","raw_affiliation_strings":["Department of Mathematical and Physical Sciences, University of Chester, CH1 4BJ, Chester, England","School of Sciences, Jimei University, Xiamen, 361021, China"],"raw_orcid":"https://orcid.org/0000-0002-5686-5017","affiliations":[{"raw_affiliation_string":"Department of Mathematical and Physical Sciences, University of Chester, CH1 4BJ, Chester, England","institution_ids":["https://openalex.org/I137265193","https://openalex.org/I4210113003"]},{"raw_affiliation_string":"School of Sciences, Jimei University, Xiamen, 361021, China","institution_ids":["https://openalex.org/I161346416"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5003578513","https://openalex.org/A5052589618"],"corresponding_institution_ids":["https://openalex.org/I137265193","https://openalex.org/I161346416","https://openalex.org/I4210113003"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.5037,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.60165663,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"88","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9997000098228455,"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":0.9987000226974487,"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/algorithm","display_name":"Algorithm","score":0.6951565742492676},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.4601278007030487},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39283692836761475},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32447052001953125},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1751873791217804}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6951565742492676},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.4601278007030487},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39283692836761475},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32447052001953125},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1751873791217804}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-021-01587-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-021-01587-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01587-9.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10915-021-01587-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-021-01587-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01587-9.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G170921898","display_name":null,"funder_award_id":"11801214","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3190956650.pdf","grobid_xml":"https://content.openalex.org/works/W3190956650.grobid-xml"},"referenced_works_count":50,"referenced_works":["https://openalex.org/W86941722","https://openalex.org/W617317968","https://openalex.org/W1510266502","https://openalex.org/W1969312973","https://openalex.org/W1976371327","https://openalex.org/W1977696410","https://openalex.org/W1998214447","https://openalex.org/W2003437637","https://openalex.org/W2004097100","https://openalex.org/W2041540906","https://openalex.org/W2043080303","https://openalex.org/W2048909372","https://openalex.org/W2052623210","https://openalex.org/W2065254635","https://openalex.org/W2071268148","https://openalex.org/W2073659542","https://openalex.org/W2082621526","https://openalex.org/W2088789193","https://openalex.org/W2091313463","https://openalex.org/W2151554918","https://openalex.org/W2165076033","https://openalex.org/W2192767319","https://openalex.org/W2504965697","https://openalex.org/W2511264644","https://openalex.org/W2567477586","https://openalex.org/W2583019075","https://openalex.org/W2601627861","https://openalex.org/W2608656286","https://openalex.org/W2615974902","https://openalex.org/W2781523636","https://openalex.org/W2783310902","https://openalex.org/W2789967849","https://openalex.org/W2794616828","https://openalex.org/W2799821673","https://openalex.org/W2803156639","https://openalex.org/W2804570618","https://openalex.org/W2894803565","https://openalex.org/W2963347032","https://openalex.org/W2963392111","https://openalex.org/W2964083141","https://openalex.org/W2964219468","https://openalex.org/W3019004624","https://openalex.org/W3027508994","https://openalex.org/W3088863664","https://openalex.org/W3098333777","https://openalex.org/W3100197187","https://openalex.org/W3103915318","https://openalex.org/W3109832867","https://openalex.org/W3135981716","https://openalex.org/W4247953052"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"continuous":[2,26],"Galerkin":[3],"time":[4,31,50,118,175],"stepping":[5,51],"method":[6,52],"is":[7,37,116,124],"introduced":[8],"and":[9,33,140],"analyzed":[10],"for":[11,95,100,161],"subdiffusion":[12],"problem":[13],"in":[14,30],"an":[15],"abstract":[16],"setting.":[17],"The":[18],"approximate":[19],"solution":[20],"will":[21],"be":[22],"sought":[23],"as":[24],"a":[25],"piecewise":[27,42],"linear":[28],"function":[29],"t":[32],"the":[34,40,48,54,105,117,127,131,162,171,174],"test":[35],"space":[36],"based":[38],"on":[39],"discontinuous":[41],"constant":[43],"functions.":[44],"We":[45],"prove":[46],"that":[47],"proposed":[49],"has":[53],"convergence":[55,122,128,160],"order":[56,123],"$$O(\\tau":[57,149],"^{1+":[58],"\\alpha":[59,62],"}),":[60],"\\,":[61],"\\in":[63],"(0,":[64],"1)$$":[65],"<mml:math":[66,112,151],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[67,113,152],"<mml:mrow>":[68,70,74,86,153],"<mml:mi>O</mml:mi>":[69,154],"<mml:mo>(</mml:mo>":[71,87,155],"<mml:msup>":[72],"<mml:mi>\u03c4</mml:mi>":[73,114,156],"<mml:mn>1</mml:mn>":[75,90],"<mml:mo>+</mml:mo>":[76],"<mml:mi>\u03b1</mml:mi>":[77,84],"</mml:mrow>":[78,81,92,93,158],"</mml:msup>":[79],"<mml:mo>)</mml:mo>":[80,91,157],"<mml:mo>,</mml:mo>":[82,89],"<mml:mspace/>":[83],"<mml:mo>\u2208</mml:mo>":[85],"<mml:mn>0</mml:mn>":[88],"</mml:math>":[94,115,159],"general":[96],"sectorial":[97],"elliptic":[98],"operators":[99],"nonsmooth":[101,163],"data":[102,181],"by":[103],"using":[104],"Laplace":[106],"transform":[107],"method,":[108],"where":[109],"$$\\tau":[110],"$$":[111],"step":[119],"size.":[120],"This":[121],"higher":[125],"than":[126],"orders":[129],"of":[130,173],"popular":[132],"convolution":[133,138],"quadrature":[134],"methods":[135,142],"(e.g.,":[136,143],"Lubich\u2019s":[137],"methods)":[139],"L-type":[141],"L1":[144],"method),":[145],"which":[146],"have":[147],"only":[148],")$$":[150],"data.":[164],"Numerical":[165],"examples":[166],"are":[167],"given":[168],"to":[169,180],"verify":[170],"robustness":[172],"discretization":[176],"schemes":[177],"with":[178],"respect":[179],"regularity.":[182]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2026-08-19T15:00:24.278416","created_date":"2025-10-10T00:00:00"}
