{"id":"https://openalex.org/W3102516647","doi":"https://doi.org/10.1080/00207160.2020.1849636","title":"Two efficient Galerkin finite element methods for the modified anomalous subdiffusion equation","display_name":"Two efficient Galerkin finite element methods for the modified anomalous subdiffusion equation","publication_year":2020,"publication_date":"2020-11-11","ids":{"openalex":"https://openalex.org/W3102516647","doi":"https://doi.org/10.1080/00207160.2020.1849636","mag":"3102516647"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2020.1849636","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2020.1849636","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","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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/A5100687057","display_name":"An Chen","orcid":"https://orcid.org/0000-0003-2165-5746"},"institutions":[{"id":"https://openalex.org/I38706770","display_name":"Guilin University of Technology","ror":"https://ror.org/03z391397","country_code":"CN","type":"education","lineage":["https://openalex.org/I38706770"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"An Chen","raw_affiliation_strings":["Guilin University of Technology","College of Science, Guilin University of Technology, Guilin, Guangxi, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Guilin University of Technology","institution_ids":["https://openalex.org/I38706770"]},{"raw_affiliation_string":"College of Science, Guilin University of Technology, Guilin, Guangxi, People's Republic of China","institution_ids":["https://openalex.org/I38706770"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100687057"],"corresponding_institution_ids":["https://openalex.org/I38706770"],"apc_list":null,"apc_paid":null,"fwci":0.0945,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.47378232,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"98","issue":"9","first_page":"1834","last_page":"1851"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9986000061035156,"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":0.9972000122070312,"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/mathematics","display_name":"Mathematics","score":0.8189109563827515},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7467362880706787},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.7149674892425537},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.6202557682991028},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5781867504119873},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.5761167407035828},{"id":"https://openalex.org/keywords/spectral-element-method","display_name":"Spectral element method","score":0.5014111995697021},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.49861884117126465},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.4929966628551483},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.4863296151161194},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.48348742723464966},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4816219210624695},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4583536684513092},{"id":"https://openalex.org/keywords/extended-finite-element-method","display_name":"Extended finite element method","score":0.44348251819610596},{"id":"https://openalex.org/keywords/crank\u2013nicolson-method","display_name":"Crank\u2013Nicolson method","score":0.4194665551185608},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.41344591975212097},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.41157108545303345},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.2557339072227478},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06692644953727722}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8189109563827515},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7467362880706787},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.7149674892425537},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.6202557682991028},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5781867504119873},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.5761167407035828},{"id":"https://openalex.org/C38961997","wikidata":"https://www.wikidata.org/wiki/Q7575186","display_name":"Spectral element method","level":4,"score":0.5014111995697021},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.49861884117126465},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.4929966628551483},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.4863296151161194},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.48348742723464966},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4816219210624695},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4583536684513092},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.44348251819610596},{"id":"https://openalex.org/C180931078","wikidata":"https://www.wikidata.org/wiki/Q588725","display_name":"Crank\u2013Nicolson method","level":3,"score":0.4194665551185608},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.41344591975212097},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.41157108545303345},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.2557339072227478},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06692644953727722},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2020.1849636","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2020.1849636","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","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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/G1738611573","display_name":null,"funder_award_id":"GLUTQD2016044","funder_id":"https://openalex.org/F4320321925","funder_display_name":"Guilin University of Technology"},{"id":"https://openalex.org/G4973715355","display_name":null,"funder_award_id":"2018GXNSFBA281020","funder_id":"https://openalex.org/F4320322768","funder_display_name":"Natural Science Foundation of Guangxi Province"},{"id":"https://openalex.org/G95889633","display_name":null,"funder_award_id":"2018GXNSFAA138121","funder_id":"https://openalex.org/F4320322768","funder_display_name":"Natural Science Foundation of Guangxi Province"}],"funders":[{"id":"https://openalex.org/F4320321925","display_name":"Guilin University of Technology","ror":"https://ror.org/03z391397"},{"id":"https://openalex.org/F4320322768","display_name":"Natural Science Foundation of Guangxi Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W902939226","https://openalex.org/W1953136735","https://openalex.org/W1977360274","https://openalex.org/W1987317750","https://openalex.org/W1998175738","https://openalex.org/W2016533177","https://openalex.org/W2031029580","https://openalex.org/W2033402214","https://openalex.org/W2037376625","https://openalex.org/W2058040466","https://openalex.org/W2073659542","https://openalex.org/W2080661489","https://openalex.org/W2082621526","https://openalex.org/W2086512227","https://openalex.org/W2111271983","https://openalex.org/W2120534562","https://openalex.org/W2120640550","https://openalex.org/W2158972649","https://openalex.org/W2406348457","https://openalex.org/W2563211547","https://openalex.org/W2605580434","https://openalex.org/W2729772172","https://openalex.org/W2765191326","https://openalex.org/W2899404163","https://openalex.org/W2963688266","https://openalex.org/W2970351530","https://openalex.org/W2981663683","https://openalex.org/W3007960120","https://openalex.org/W3012491034","https://openalex.org/W3148434010"],"related_works":["https://openalex.org/W2376732695","https://openalex.org/W2565231037","https://openalex.org/W1989473560","https://openalex.org/W1977906733","https://openalex.org/W1567939749","https://openalex.org/W2185206193","https://openalex.org/W3196813885","https://openalex.org/W2071835335","https://openalex.org/W2616764899","https://openalex.org/W2096199043"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,76],"consider":[4],"the":[5,9,16,32,42,49,53,72,90,97],"numerical":[6,80],"approximation":[7],"of":[8,92],"modified":[10],"anomalous":[11],"subdiffusion":[12],"model":[13],"which":[14],"involves":[15],"Riemann\u2013Liouville":[17],"derivatives":[18],"in":[19,39,45],"time.":[20],"We":[21],"propose":[22],"two":[23],"robust":[24],"fully":[25,64],"discrete":[26,65],"finite":[27,36,85],"element":[28,37,86],"methods":[29,94],"by":[30,48],"employing":[31],"piecewise":[33],"linear":[34],"Galerkin":[35],"method":[38,87],"space":[40],"and":[41,52,63,95],"convolution":[43],"quadrature":[44],"time":[46],"generated":[47],"backward":[50,55],"Euler":[51],"second-order":[54],"difference":[56],"methods.":[57],"The":[58],"error":[59],"estimates":[60],"for":[61],"semidiscrete":[62],"schemes":[66,81],"are":[67],"investigated":[68],"with":[69,82],"respect":[70],"to":[71,88],"data":[73],"regularity.":[74],"Furthermore,":[75],"numerically":[77],"compare":[78],"our":[79,93],"a":[83],"Crank\u2013Nicolson":[84],"illustrate":[89],"efficiency":[91],"confirm":[96],"theoretical":[98],"results.":[99]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}
