{"id":"https://openalex.org/W4410608375","doi":"https://doi.org/10.1080/00207160.2025.2507678","title":"Fast two-grid finite volume element algorithms combined with Crank-Nicolson scheme for the nonlinear time fractional mobile/immobile transport model","display_name":"Fast two-grid finite volume element algorithms combined with Crank-Nicolson scheme for the nonlinear time fractional mobile/immobile transport model","publication_year":2025,"publication_date":"2025-05-21","ids":{"openalex":"https://openalex.org/W4410608375","doi":"https://doi.org/10.1080/00207160.2025.2507678"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2025.2507678","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2025.2507678","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/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":["Inner Mongolia University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inner Mongolia University","institution_ids":["https://openalex.org/I2722730"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060717803","display_name":"Jie Zhao","orcid":"https://orcid.org/0000-0002-0508-9601"},"institutions":[{"id":"https://openalex.org/I4210088341","display_name":"University of Finance and Economics","ror":"https://ror.org/005d8s603","country_code":"MN","type":"education","lineage":["https://openalex.org/I4210088341"]}],"countries":["MN"],"is_corresponding":false,"raw_author_name":"Jie Zhao","raw_affiliation_strings":["Inner Mongolia University of Finance and Economics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inner Mongolia University of Finance and Economics","institution_ids":["https://openalex.org/I4210088341"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103002350","display_name":"Hong Li","orcid":"https://orcid.org/0000-0001-6819-3038"},"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":"Hong Li","raw_affiliation_strings":["Inner Mongolia University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inner Mongolia University","institution_ids":["https://openalex.org/I2722730"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100355931","display_name":"Yang Liu","orcid":"https://orcid.org/0000-0002-5649-9483"},"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":["Inner Mongolia University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inner Mongolia University","institution_ids":["https://openalex.org/I2722730"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103002350"],"corresponding_institution_ids":["https://openalex.org/I2722730"],"apc_list":null,"apc_paid":null,"fwci":3.5589,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.9234831,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"102","issue":"10","first_page":"1563","last_page":"1584"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9994000196456909,"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":0.9994000196456909,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7118925452232361},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6964905858039856},{"id":"https://openalex.org/keywords/crank\u2013nicolson-method","display_name":"Crank\u2013Nicolson method","score":0.6602737903594971},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5675909519195557},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.547383725643158},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5358446836471558},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4587351381778717},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4552111327648163},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.4318965673446655},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3828126788139343},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.25125497579574585},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.20498818159103394},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.081868976354599},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06713405251502991},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.06397449970245361}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7118925452232361},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6964905858039856},{"id":"https://openalex.org/C180931078","wikidata":"https://www.wikidata.org/wiki/Q588725","display_name":"Crank\u2013Nicolson method","level":3,"score":0.6602737903594971},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5675909519195557},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.547383725643158},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5358446836471558},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4587351381778717},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4552111327648163},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.4318965673446655},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3828126788139343},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25125497579574585},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.20498818159103394},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.081868976354599},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06713405251502991},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.06397449970245361},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2025.2507678","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2025.2507678","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/G1646297626","display_name":null,"funder_award_id":"2024MS01013","funder_id":"https://openalex.org/F4320322868","funder_display_name":"Natural Science Foundation of Inner Mongolia"},{"id":"https://openalex.org/G1979918791","display_name":null,"funder_award_id":"12161063, 12461080, 11701299","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/F4320322868","display_name":"Natural Science Foundation of Inner Mongolia","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W1521920611","https://openalex.org/W1969312973","https://openalex.org/W1980455776","https://openalex.org/W2001011967","https://openalex.org/W2017786109","https://openalex.org/W2032474987","https://openalex.org/W2036818032","https://openalex.org/W2085422562","https://openalex.org/W2086512227","https://openalex.org/W2089766265","https://openalex.org/W2103296601","https://openalex.org/W2143874584","https://openalex.org/W2151939722","https://openalex.org/W2161513111","https://openalex.org/W2165076033","https://openalex.org/W2166757998","https://openalex.org/W2188779374","https://openalex.org/W2277830160","https://openalex.org/W2292103023","https://openalex.org/W2503319909","https://openalex.org/W2586612085","https://openalex.org/W2612667563","https://openalex.org/W2754207224","https://openalex.org/W2807246622","https://openalex.org/W2928839578","https://openalex.org/W2971942511","https://openalex.org/W2981663683","https://openalex.org/W2982289212","https://openalex.org/W2996527000","https://openalex.org/W2999341757","https://openalex.org/W3033861800","https://openalex.org/W3043208752","https://openalex.org/W3048535844","https://openalex.org/W3092112468","https://openalex.org/W3103882064","https://openalex.org/W3119357403","https://openalex.org/W3154762144","https://openalex.org/W3197756214","https://openalex.org/W3205545207","https://openalex.org/W3213990007","https://openalex.org/W4220943094","https://openalex.org/W4225858257","https://openalex.org/W4240003552","https://openalex.org/W4285396339","https://openalex.org/W4306641995","https://openalex.org/W4309048310","https://openalex.org/W4405041668"],"related_works":["https://openalex.org/W4223970227","https://openalex.org/W4382021032","https://openalex.org/W2026628742","https://openalex.org/W940193414","https://openalex.org/W2326356320","https://openalex.org/W3049665010","https://openalex.org/W4390971841","https://openalex.org/W2081976282","https://openalex.org/W4392355086","https://openalex.org/W2163264797"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"fast":[3,35,98,141],"time":[4,20],"second-order":[5],"two-grid":[6,70,99],"algorithms":[7,36,76,101,142],"are":[8,77,91,134,143],"proposed":[9,140],"for":[10,68],"solving":[11,38,53],"the":[12,18,25,31,39,43,54,69,80,85,97,110,120,127,139],"nonlinear":[13,40],"mobile/immobile":[14],"transport":[15],"model":[16],"with":[17],"Riemann-Liouville":[19],"fractional":[21],"derivative":[22],"by":[23],"using":[24],"finite":[26,72],"volume":[27,73],"element":[28,74],"algorithm":[29],"and":[30,51,79,88,113,124],"Crank-Nicolson":[32,71],"scheme.":[33],"The":[34,65,131],"involve":[37],"system":[41,56],"on":[42,57],"spatial":[44,58,111],"coarse":[45,112],"grid":[46,48,60,62,115],"(with":[47,61],"size":[49,63],"H)":[50],"then":[52],"linearized":[55],"fine":[59,114],"h).":[64],"stability":[66],"results":[67,133],"(CNFVE)":[75],"given,":[78],"optimal":[81,105],"error":[82],"estimates":[83],"in":[84],"discrete":[86,121,128],"L\u221e(L2(\u03a9))":[87,122],"L2(H1(\u03a9))":[89,129],"norms":[90],"obtained.":[92],"It":[93],"is":[94],"shown":[95],"that":[96,138],"CNFVE":[100],"can":[102],"achieve":[103],"asymptotically":[104],"approximation,":[106],"as":[107,109],"long":[108],"sizes":[116],"satisfy":[117],"H=O(h1/2)":[118],"(in":[119,126],"norm)":[123],"H=O(h1/4)":[125],"norm).":[130],"numerical":[132],"given":[135],"to":[136],"validate":[137],"very":[144],"effective.":[145]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3}],"updated_date":"2026-06-14T06:11:07.267592","created_date":"2025-10-10T00:00:00"}