{"id":"https://openalex.org/W2084287481","doi":"https://doi.org/10.1142/s1793962314500226","title":"Application of low-dimensional finite element method to fractional diffusion equation","display_name":"Application of low-dimensional finite element method to fractional diffusion equation","publication_year":2014,"publication_date":"2014-07-29","ids":{"openalex":"https://openalex.org/W2084287481","doi":"https://doi.org/10.1142/s1793962314500226","mag":"2084287481"},"language":"en","primary_location":{"id":"doi:10.1142/s1793962314500226","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793962314500226","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/A5011189615","display_name":"Jincun Liu","orcid":"https://orcid.org/0000-0002-2872-4911"},"institutions":[{"id":"https://openalex.org/I2722730","display_name":"Inner Mongolia University","ror":"https://ror.org/0106qb496","country_code":"CN","type":"education","lineage":["https://openalex.org/I2722730"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jincun Liu","raw_affiliation_strings":["School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China","institution_ids":["https://openalex.org/I2722730"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058935935","display_name":"Hong Li","orcid":"https://orcid.org/0000-0002-9832-0496"},"institutions":[{"id":"https://openalex.org/I2722730","display_name":"Inner Mongolia University","ror":"https://ror.org/0106qb496","country_code":"CN","type":"education","lineage":["https://openalex.org/I2722730"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hong Li","raw_affiliation_strings":["School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China","institution_ids":["https://openalex.org/I2722730"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079134023","display_name":"Zhichao Fang","orcid":"https://orcid.org/0000-0001-8436-698X"},"institutions":[{"id":"https://openalex.org/I2722730","display_name":"Inner Mongolia University","ror":"https://ror.org/0106qb496","country_code":"CN","type":"education","lineage":["https://openalex.org/I2722730"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhichao Fang","raw_affiliation_strings":["School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China","institution_ids":["https://openalex.org/I2722730"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054988044","display_name":"Yang Liu","orcid":"https://orcid.org/0000-0001-8218-0196"},"institutions":[{"id":"https://openalex.org/I2722730","display_name":"Inner Mongolia University","ror":"https://ror.org/0106qb496","country_code":"CN","type":"education","lineage":["https://openalex.org/I2722730"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang Liu","raw_affiliation_strings":["School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China","institution_ids":["https://openalex.org/I2722730"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5011189615"],"corresponding_institution_ids":["https://openalex.org/I2722730"],"apc_list":null,"apc_paid":null,"fwci":0.7245,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.71995333,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"05","issue":"04","first_page":"1450022","last_page":"1450022"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9994999766349792,"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":0.9994999766349792,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9987000226974487,"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/finite-element-method","display_name":"Finite element method","score":0.8010194301605225},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6216360330581665},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6023119688034058},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5359189510345459},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.4946448504924774},{"id":"https://openalex.org/keywords/proper-orthogonal-decomposition","display_name":"Proper orthogonal decomposition","score":0.49063578248023987},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.48620742559432983},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4757344722747803},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.46989819407463074},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.4436336159706116},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.42875349521636963},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4160543382167816},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.4124950170516968},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2448274791240692},{"id":"https://openalex.org/keywords/point-of-delivery","display_name":"Point of delivery","score":0.2153845727443695},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17735737562179565},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11053737998008728}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.8010194301605225},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6216360330581665},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6023119688034058},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5359189510345459},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.4946448504924774},{"id":"https://openalex.org/C2984998066","wikidata":"https://www.wikidata.org/wiki/Q105037988","display_name":"Proper orthogonal decomposition","level":3,"score":0.49063578248023987},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.48620742559432983},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4757344722747803},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.46989819407463074},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.4436336159706116},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.42875349521636963},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4160543382167816},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.4124950170516968},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2448274791240692},{"id":"https://openalex.org/C137776501","wikidata":"https://www.wikidata.org/wiki/Q7208270","display_name":"Point of delivery","level":2,"score":0.2153845727443695},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17735737562179565},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11053737998008728},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.0},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793962314500226","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793962314500226","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":[{"display_name":"Peace, Justice and strong institutions","score":0.7900000214576721,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322868","display_name":"Natural Science Foundation of Inner Mongolia","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W110340196","https://openalex.org/W1418158239","https://openalex.org/W1530054495","https://openalex.org/W1553338987","https://openalex.org/W1633869374","https://openalex.org/W1964028905","https://openalex.org/W1966258563","https://openalex.org/W1966513244","https://openalex.org/W1969312973","https://openalex.org/W1974258811","https://openalex.org/W1977696410","https://openalex.org/W1984617383","https://openalex.org/W1989951672","https://openalex.org/W2000659785","https://openalex.org/W2006543616","https://openalex.org/W2017745440","https://openalex.org/W2019324632","https://openalex.org/W2044555722","https://openalex.org/W2045231411","https://openalex.org/W2071032561","https://openalex.org/W2074077397","https://openalex.org/W2084142728","https://openalex.org/W2088216803","https://openalex.org/W2091740033","https://openalex.org/W2093685032","https://openalex.org/W2104736025","https://openalex.org/W2112823474","https://openalex.org/W2118157144","https://openalex.org/W2127684492","https://openalex.org/W2135346934","https://openalex.org/W2140693310","https://openalex.org/W2165076033","https://openalex.org/W2732661672","https://openalex.org/W2787959293","https://openalex.org/W3145074154","https://openalex.org/W4242273588"],"related_works":["https://openalex.org/W2461877434","https://openalex.org/W2372758580","https://openalex.org/W4238156215","https://openalex.org/W2044906932","https://openalex.org/W1964028905","https://openalex.org/W1986572238","https://openalex.org/W2014319192","https://openalex.org/W2377880252","https://openalex.org/W2026610487","https://openalex.org/W2084287481"],"abstract_inverted_index":{"Classical":[0],"finite":[1],"element":[2],"method":[3,58,87],"(FEM)":[4],"has":[5,17,59],"been":[6],"applied":[7],"to":[8,94],"solve":[9],"some":[10],"fractional":[11,50,112],"differential":[12,113],"equations,":[13],"but":[14],"its":[15],"scheme":[16],"too":[18],"many":[19],"degrees":[20],"of":[21,31,39,62,72,85,100],"freedom.":[22],"In":[23],"this":[24],"paper,":[25],"a":[26],"low-dimensional":[27,102],"FEM,":[28],"whose":[29],"number":[30],"basis":[32],"functions":[33],"is":[34,45,74,80,88,92],"reduced":[35],"by":[36],"the":[37,48,60,70,77,86,96,101,110],"theory":[38],"proper":[40],"orthogonal":[41],"decomposition":[42],"(POD)":[43],"technique,":[44],"proposed":[46],"for":[47,109],"time":[49,79,111],"diffusion":[51],"equation":[52],"in":[53,104],"two-dimensional":[54],"space.":[55],"The":[56],"presented":[57],"properties":[61],"low":[63],"dimensions":[64],"and":[65,76,98],"high":[66],"accuracy":[67],"so":[68],"that":[69],"amount":[71],"computation":[73],"decreased":[75],"calculation":[78],"saved.":[81],"Moreover,":[82],"error":[83],"estimation":[84],"obtained.":[89],"Numerical":[90],"example":[91],"given":[93],"illustrate":[95],"feasibility":[97],"validity":[99],"FEM":[103,108],"comparison":[105],"with":[106],"traditional":[107],"equations.":[114]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}