{"id":"https://openalex.org/W2342612762","doi":"https://doi.org/10.1515/cmam-2016-0017","title":"Tailored Finite Point Method for Parabolic Problems","display_name":"Tailored Finite Point Method for Parabolic Problems","publication_year":2016,"publication_date":"2016-04-27","ids":{"openalex":"https://openalex.org/W2342612762","doi":"https://doi.org/10.1515/cmam-2016-0017","mag":"2342612762"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2016-0017","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2016-0017","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied 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/A5065270536","display_name":"Zhongyi Huang","orcid":"https://orcid.org/0000-0002-5623-4864"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhongyi Huang","raw_affiliation_strings":["Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089169772","display_name":"Yi Yang","orcid":"https://orcid.org/0000-0003-1858-4641"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yi Yang","raw_affiliation_strings":["Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065270536"],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":1.8254,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.83385384,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"16","issue":"4","first_page":"543","last_page":"562"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998999834060669,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7155267000198364},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5516287088394165},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5315746068954468},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.5170103311538696},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5123327970504761},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5088363289833069},{"id":"https://openalex.org/keywords/finite-difference-scheme","display_name":"Finite difference scheme","score":0.497334748506546},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.48896801471710205},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4822321832180023},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.4821147918701172},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.46340039372444153},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4529295861721039},{"id":"https://openalex.org/keywords/finite-difference-coefficient","display_name":"Finite difference coefficient","score":0.4385346472263336},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.42240482568740845},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.42180579900741577},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3968445062637329},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21296608448028564},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.187366783618927},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13133350014686584}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7155267000198364},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5516287088394165},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5315746068954468},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.5170103311538696},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5123327970504761},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5088363289833069},{"id":"https://openalex.org/C2988766672","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference scheme","level":2,"score":0.497334748506546},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.48896801471710205},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4822321832180023},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.4821147918701172},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.46340039372444153},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4529295861721039},{"id":"https://openalex.org/C108268861","wikidata":"https://www.wikidata.org/wiki/Q1747602","display_name":"Finite difference coefficient","level":4,"score":0.4385346472263336},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.42240482568740845},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.42180579900741577},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3968445062637329},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21296608448028564},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.187366783618927},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13133350014686584},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2016-0017","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2016-0017","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1613156395","display_name":null,"funder_award_id":"91330203","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3225641615","display_name":null,"funder_award_id":"11322113","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1595598994","https://openalex.org/W2029414071","https://openalex.org/W2053647988","https://openalex.org/W2054071080","https://openalex.org/W2077946970","https://openalex.org/W2079767381","https://openalex.org/W2081862397","https://openalex.org/W2089086358","https://openalex.org/W2099283728","https://openalex.org/W2115083628","https://openalex.org/W2160326158","https://openalex.org/W2482071863","https://openalex.org/W2584417483","https://openalex.org/W2607734124"],"related_works":["https://openalex.org/W2330640442","https://openalex.org/W2372700288","https://openalex.org/W2983915667","https://openalex.org/W2085654163","https://openalex.org/W2392533133","https://openalex.org/W2370641521","https://openalex.org/W2376771521","https://openalex.org/W2766501744","https://openalex.org/W2363145727","https://openalex.org/W2756693448"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"we":[4,42,72],"propose":[5],"a":[6],"class":[7],"of":[8,19,39,92],"new":[9,56],"tailored":[10,28],"finite":[11,23,48],"point":[12,24],"methods":[13],"(TFPM)":[14],"for":[15,79],"the":[16,31,37,46,68,74,80,88],"numerical":[17,85],"solution":[18],"parabolic":[20],"equations.":[21],"Our":[22,84],"method":[25],"has":[26],"been":[27],"based":[29],"on":[30],"local":[32],"exponential":[33],"basis":[34],"functions.":[35],"By":[36],"idea":[38],"our":[40],"TFPM,":[41],"can":[43,52],"recover":[44],"all":[45],"traditional":[47],"difference":[49],"schemes.":[50],"We":[51],"also":[53],"construct":[54,73],"some":[55],"TFPM":[57,77],"schemes":[58],"with":[59,67],"better":[60],"stability":[61],"condition":[62],"and":[63,90],"accuracy.":[64],"Furthermore,":[65],"combining":[66],"Shishkin":[69],"mesh":[70],"technique,":[71],"uniformly":[75],"convergent":[76],"scheme":[78],"convection-dominant":[81],"convection-diffusion":[82],"problem.":[83],"examples":[86],"show":[87],"efficiency":[89],"reliability":[91],"TFPM.":[93]},"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
