{"id":"https://openalex.org/W3038892232","doi":"https://doi.org/10.1142/s1793962320300010","title":"Finite element methods for fractional diffusion equations","display_name":"Finite element methods for fractional diffusion equations","publication_year":2020,"publication_date":"2020-06-29","ids":{"openalex":"https://openalex.org/W3038892232","doi":"https://doi.org/10.1142/s1793962320300010","mag":"3038892232"},"language":"en","primary_location":{"id":"doi:10.1142/s1793962320300010","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793962320300010","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modeling, Simulation, and Scientific Computing","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/A5115565864","display_name":"Y\u00fce Zhao","orcid":"https://orcid.org/0000-0002-5940-3651"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yue Zhao","raw_affiliation_strings":["LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China","School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010502099","display_name":"Chen Shen","orcid":"https://orcid.org/0000-0002-4325-5957"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen Shen","raw_affiliation_strings":["School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan 411105, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan 411105, P. R. China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042725621","display_name":"Min Qu","orcid":null},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Min Qu","raw_affiliation_strings":["School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan 411105, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan 411105, P. R. China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108644227","display_name":"Weiping Bu","orcid":null},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weiping Bu","raw_affiliation_strings":["School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan 411105, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan 411105, P. R. China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111634036","display_name":"Yifa Tang","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yifa Tang","raw_affiliation_strings":["LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China","School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. China","institution_ids":["https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1266,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.49730636,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"11","issue":"04","first_page":"2030001","last_page":"2030001"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"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":1.0,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9969000220298767,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9958999752998352,"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/fractional-calculus","display_name":"Fractional calculus","score":0.6049594879150391},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5864423513412476},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.548721194267273},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5176037549972534},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4995152950286865},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4548424482345581},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43003493547439575},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.41064226627349854},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20445126295089722},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.08540457487106323}],"concepts":[{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6049594879150391},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5864423513412476},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.548721194267273},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5176037549972534},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4995152950286865},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4548424482345581},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43003493547439575},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.41064226627349854},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20445126295089722},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08540457487106323},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"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/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793962320300010","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793962320300010","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modeling, Simulation, and Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5199999809265137,"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure"}],"awards":[{"id":"https://openalex.org/G1542429742","display_name":"\u7b49\u79bb\u5b50\u4f53\u7269\u7406\u4e2d\u7684\u8f9b\u7b97\u6cd5\u4e0e\u5e73\u5747\u65b9\u6cd5","funder_award_id":"11771438","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6549691289","display_name":null,"funder_award_id":"2018JJ3491","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G7346749444","display_name":null,"funder_award_id":"11601460","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"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":120,"referenced_works":["https://openalex.org/W374977727","https://openalex.org/W820881791","https://openalex.org/W902939226","https://openalex.org/W1252767471","https://openalex.org/W1508646408","https://openalex.org/W1574718224","https://openalex.org/W1776097589","https://openalex.org/W1880690653","https://openalex.org/W1966513244","https://openalex.org/W1969312973","https://openalex.org/W1974043434","https://openalex.org/W1976371327","https://openalex.org/W1991982189","https://openalex.org/W2000659785","https://openalex.org/W2001509015","https://openalex.org/W2004467399","https://openalex.org/W2012170120","https://openalex.org/W2019324632","https://openalex.org/W2019543280","https://openalex.org/W2028179802","https://openalex.org/W2032744100","https://openalex.org/W2033593438","https://openalex.org/W2034839545","https://openalex.org/W2037973974","https://openalex.org/W2039427414","https://openalex.org/W2043080303","https://openalex.org/W2043617602","https://openalex.org/W2056829543","https://openalex.org/W2065232540","https://openalex.org/W2070505112","https://openalex.org/W2071268148","https://openalex.org/W2080928512","https://openalex.org/W2081871678","https://openalex.org/W2083046996","https://openalex.org/W2084142728","https://openalex.org/W2088114223","https://openalex.org/W2088216803","https://openalex.org/W2090539565","https://openalex.org/W2092146111","https://openalex.org/W2092912961","https://openalex.org/W2104736025","https://openalex.org/W2111271983","https://openalex.org/W2124718863","https://openalex.org/W2130170219","https://openalex.org/W2136655753","https://openalex.org/W2139559416","https://openalex.org/W2140057174","https://openalex.org/W2144367930","https://openalex.org/W2165076033","https://openalex.org/W2172034033","https://openalex.org/W2256040747","https://openalex.org/W2267852856","https://openalex.org/W2291079924","https://openalex.org/W2294672943","https://openalex.org/W2297442058","https://openalex.org/W2299470766","https://openalex.org/W2308477722","https://openalex.org/W2312385896","https://openalex.org/W2325660078","https://openalex.org/W2397817385","https://openalex.org/W2480746121","https://openalex.org/W2523295918","https://openalex.org/W2535408367","https://openalex.org/W2582904625","https://openalex.org/W2586401190","https://openalex.org/W2588029474","https://openalex.org/W2592808318","https://openalex.org/W2605752662","https://openalex.org/W2608656286","https://openalex.org/W2613087776","https://openalex.org/W2615974902","https://openalex.org/W2624969825","https://openalex.org/W2626148257","https://openalex.org/W2728907612","https://openalex.org/W2729772172","https://openalex.org/W2737657582","https://openalex.org/W2753466262","https://openalex.org/W2753893094","https://openalex.org/W2789611442","https://openalex.org/W2792503105","https://openalex.org/W2792947986","https://openalex.org/W2793924997","https://openalex.org/W2794616828","https://openalex.org/W2801192398","https://openalex.org/W2802398486","https://openalex.org/W2802986201","https://openalex.org/W2804149282","https://openalex.org/W2806752574","https://openalex.org/W2870487173","https://openalex.org/W2898200204","https://openalex.org/W2898343465","https://openalex.org/W2905383021","https://openalex.org/W2914535700","https://openalex.org/W2917604905","https://openalex.org/W2941043721","https://openalex.org/W2946971190","https://openalex.org/W2950965409","https://openalex.org/W2954466520","https://openalex.org/W2963142826","https://openalex.org/W2963309992","https://openalex.org/W2963907193","https://openalex.org/W2964219468","https://openalex.org/W2965184132","https://openalex.org/W2971718279","https://openalex.org/W2972043782","https://openalex.org/W2973471320","https://openalex.org/W2982710089","https://openalex.org/W2998692622","https://openalex.org/W3000311770","https://openalex.org/W3000618690","https://openalex.org/W3098333777","https://openalex.org/W3101361006","https://openalex.org/W3102260850","https://openalex.org/W3103229763","https://openalex.org/W3105594617","https://openalex.org/W3105657163","https://openalex.org/W4230205099","https://openalex.org/W4249242116","https://openalex.org/W4253541821","https://openalex.org/W4361794280"],"related_works":["https://openalex.org/W2082446734","https://openalex.org/W4313560640","https://openalex.org/W2253351617","https://openalex.org/W4246784705","https://openalex.org/W2055836843","https://openalex.org/W1734603769","https://openalex.org/W4213231742","https://openalex.org/W2922935260","https://openalex.org/W2066116605","https://openalex.org/W1592131421"],"abstract_inverted_index":{"Due":[0],"to":[1],"the":[2,21,80,83,86],"successful":[3],"applications":[4],"in":[5,16],"engineering,":[6],"physics,":[7],"biology,":[8],"finance,":[9],"etc.,":[10],"there":[11],"has":[12],"been":[13],"substantial":[14],"interest":[15],"fractional":[17,66,69],"diffusion":[18,70],"equations":[19,40],"over":[20],"past":[22],"few":[23],"decades,":[24],"and":[25,29,32,43,67,85],"literatures":[26],"on":[27,52,79],"developing":[28],"analyzing":[30],"efficient":[31],"accurate":[33],"numerical":[34],"methods":[35,55],"for":[36,56],"reliably":[37],"simulating":[38],"such":[39],"are":[41,60],"vast":[42],"fast":[44,87],"growing.":[45],"This":[46],"paper":[47],"gives":[48],"a":[49],"concise":[50],"overview":[51],"finite":[53],"element":[54],"these":[57],"equations,":[58],"which":[59],"divided":[61],"into":[62],"time":[63],"fractional,":[64],"space":[65],"time-space":[68],"equations.":[71],"Besides,":[72],"we":[73],"also":[74],"involve":[75],"some":[76],"relevant":[77],"topics":[78],"regularity":[81],"theory,":[82],"well-posedness,":[84],"algorithm.":[88]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}