{"id":"https://openalex.org/W2149756576","doi":"https://doi.org/10.1155/2013/385463","title":"Finite Element Multigrid Method for the Boundary Value Problem of Fractional Advection Dispersion Equation","display_name":"Finite Element Multigrid Method for the Boundary Value Problem of Fractional Advection Dispersion Equation","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2149756576","doi":"https://doi.org/10.1155/2013/385463","mag":"2149756576"},"language":"en","primary_location":{"id":"doi:10.1155/2013/385463","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/385463","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/385463.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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 Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2013/385463.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102892616","display_name":"Zhou Zhi-qiang","orcid":"https://orcid.org/0000-0001-5031-5041"},"institutions":[{"id":"https://openalex.org/I12393601","display_name":"Huaihua University","ror":"https://ror.org/04zn6xq74","country_code":"CN","type":"education","lineage":["https://openalex.org/I12393601"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhiqiang Zhou","raw_affiliation_strings":["Department of Mathematics, Huaihua University, Huaihua 418008"],"raw_orcid":"https://orcid.org/0000-0001-5031-5041","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Huaihua University, Huaihua 418008","institution_ids":["https://openalex.org/I12393601"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102339782","display_name":"WU Hong-ying","orcid":null},"institutions":[{"id":"https://openalex.org/I12393601","display_name":"Huaihua University","ror":"https://ror.org/04zn6xq74","country_code":"CN","type":"education","lineage":["https://openalex.org/I12393601"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongying Wu","raw_affiliation_strings":["Department of Mathematics, Huaihua University, Huaihua 418008"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Huaihua University, Huaihua 418008","institution_ids":["https://openalex.org/I12393601"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102892616"],"corresponding_institution_ids":["https://openalex.org/I12393601"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":2.4335,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.87713559,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"8"},"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":0.9995999932289124,"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/mathematics","display_name":"Mathematics","score":0.7189976572990417},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6441634297370911},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5619649887084961},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5235395431518555},{"id":"https://openalex.org/keywords/advection","display_name":"Advection","score":0.5130332708358765},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.47756749391555786},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.4759913682937622},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.45834892988204956},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4311137795448303},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.428778737783432},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42706114053726196},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4120432734489441},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.2624224126338959},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23398450016975403},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10485774278640747},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09532970190048218},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.08221125602722168},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.06929609179496765}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7189976572990417},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6441634297370911},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5619649887084961},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5235395431518555},{"id":"https://openalex.org/C5072599","wikidata":"https://www.wikidata.org/wiki/Q379788","display_name":"Advection","level":2,"score":0.5130332708358765},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.47756749391555786},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.4759913682937622},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.45834892988204956},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4311137795448303},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.428778737783432},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42706114053726196},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4120432734489441},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2624224126338959},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23398450016975403},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10485774278640747},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09532970190048218},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.08221125602722168},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.06929609179496765},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2013/385463","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/385463","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/385463.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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 Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1394808009","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1394808009","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:385463","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2013/385463.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:37abbb0fb8dc4ef68e00ec388cd881bf","is_oa":true,"landing_page_url":"https://doaj.org/article/37abbb0fb8dc4ef68e00ec388cd881bf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/385463","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/385463","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/385463.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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 Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2149756576.pdf","grobid_xml":"https://content.openalex.org/works/W2149756576.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W577640155","https://openalex.org/W1492326914","https://openalex.org/W1550268283","https://openalex.org/W1553338987","https://openalex.org/W1966513244","https://openalex.org/W1967011851","https://openalex.org/W1983959946","https://openalex.org/W1999695483","https://openalex.org/W2004467399","https://openalex.org/W2004872575","https://openalex.org/W2024606917","https://openalex.org/W2091740033","https://openalex.org/W2096245154","https://openalex.org/W2099111135","https://openalex.org/W2104736025","https://openalex.org/W2127769310","https://openalex.org/W2138050970","https://openalex.org/W2787959293","https://openalex.org/W4250501155","https://openalex.org/W4298065537"],"related_works":["https://openalex.org/W2501988474","https://openalex.org/W2021837978","https://openalex.org/W2071331562","https://openalex.org/W2295047789","https://openalex.org/W2021116964","https://openalex.org/W2116481540","https://openalex.org/W240948612","https://openalex.org/W4255218996","https://openalex.org/W425311387","https://openalex.org/W1559891132"],"abstract_inverted_index":{"The":[0],"stationary":[1],"fractional":[2],"advection":[3],"dispersion":[4],"equation":[5],"is":[6,20],"discretized":[7],"by":[8],"linear":[9],"finite":[10],"element":[11],"scheme,":[12],"and":[13,33,144,158],"a":[14],"full":[15],"V-cycle":[16],"multigrid":[17],"method":[18],"(FV-MGM)":[19],"proposed":[21],"to":[22,153],"solve":[23],"the":[24,31,43,155,161],"resulting":[25],"system.":[26],"Some":[27],"useful":[28],"properties":[29,40],"of":[30,160],"approximation":[32],"smoothing":[34],"operators":[35],"are":[36,151],"proved.":[37],"Using":[38],"these":[39],"we":[41],"derive":[42],"convergence":[44,156],"results":[45],"in":[46],"both":[47],"<svg":[48],"style=\"vertical-align:-0.0pt;width:16.1625px;\"":[49],"id=\"M1\"":[50],"height=\"15.8375\"":[51],"version=\"1.1\"":[52],"viewBox=\"0":[53],"0":[54,93,120,128,137],"16.1625":[55],"15.8375\"":[56],"width=\"16.1625\"":[57],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"":[58],"xmlns=\"http://www.w3.org/2000/svg\">":[59],"<g":[60,100],"transform=\"matrix(.017,-0,0,-.017,.062,15.775)\"><path":[61],"id=\"x1D43F\"":[62],"d=\"M559":[63],"163q-23":[64],"-66":[65],"-68":[66],"-163h-474l6":[67],"26q62":[68],"4":[69],"79.5":[70],"19.5t28.5":[71],"75.5l78":[72],"409q7":[73],"35":[74],"8.5":[75],"49t-8":[76],"25t-24":[77],"13t-51.5":[78],"5l5":[79],"28h266l-6":[80],"-28q-65":[81],"-5":[82],"-79.5":[83],"-18t-25.5":[84],"-74l-76":[85],"-406q-10":[86],"-57":[87],"14":[88],"-75q12":[89],"-13":[90],"96":[91],"-13q93":[92],"126":[94],"29q41":[95],"40":[96],"76":[97],"109z\"":[98],"/></g>":[99,141],"transform=\"matrix(.012,-0,0,-.012,9.763,7.613)\"><path":[101],"id=\"x32\"":[102],"d=\"M412":[103],"140l28":[104],"-9q0":[105],"-2":[106],"-35":[107],"-131h-373v23q112":[108],"112":[109],"161":[110],"170q59":[111],"70":[112],"92":[113],"127t33":[114],"115q0":[115],"63":[116],"-31":[117],"98t-86":[118],"35q-75":[119],"-137":[121],"-93l-22":[122],"20l57":[123],"81q55":[124],"59":[125],"135":[126],"59q69":[127],"118.5":[129],"-46.5t49.5":[130],"-122.5q0":[131],"-62":[132],"-29.5":[133],"-114t-102.5":[134],"-130l-141":[135],"-149h186q42":[136],"58.5":[138],"10.5t38.5":[139],"56.5z\"":[140],"</svg>":[142],"norm":[143,146],"energy":[145],"for":[147],"FV-MGM.":[148],"Numerical":[149],"examples":[150],"given":[152],"demonstrate":[154],"rate":[157],"efficiency":[159],"method.":[162]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
