{"id":"https://openalex.org/W2956155330","doi":"https://doi.org/10.1080/00207160.2019.1639676","title":"Superconvergence analysis of FEM for 2D multi-term time fractional diffusion-wave equations with variable coefficient","display_name":"Superconvergence analysis of FEM for 2D multi-term time fractional diffusion-wave equations with variable coefficient","publication_year":2019,"publication_date":"2019-07-05","ids":{"openalex":"https://openalex.org/W2956155330","doi":"https://doi.org/10.1080/00207160.2019.1639676","mag":"2956155330"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2019.1639676","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2019.1639676","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/A5100645756","display_name":"Yuanyuan Shi","orcid":"https://orcid.org/0000-0002-4836-6752"},"institutions":[{"id":"https://openalex.org/I903994226","display_name":"Xuchang University","ror":"https://ror.org/03k174p87","country_code":"CN","type":"education","lineage":["https://openalex.org/I903994226"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Y. H. Shi","raw_affiliation_strings":["School of Mathematics and Statistics, Xuchang University, Xuchang, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xuchang University, Xuchang, People's Republic of China","institution_ids":["https://openalex.org/I903994226"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103726418","display_name":"Yinghua Zhao","orcid":"https://orcid.org/0009-0005-5936-7688"},"institutions":[{"id":"https://openalex.org/I903994226","display_name":"Xuchang University","ror":"https://ror.org/03k174p87","country_code":"CN","type":"education","lineage":["https://openalex.org/I903994226"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Y. M. Zhao","raw_affiliation_strings":["School of Mathematics and Statistics, Xuchang University, Xuchang, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xuchang University, Xuchang, People's Republic of China","institution_ids":["https://openalex.org/I903994226"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020646953","display_name":"F. L. Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I903994226","display_name":"Xuchang University","ror":"https://ror.org/03k174p87","country_code":"CN","type":"education","lineage":["https://openalex.org/I903994226"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"F. L. Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Xuchang University, Xuchang, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xuchang University, Xuchang, People's Republic of China","institution_ids":["https://openalex.org/I903994226"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101877864","display_name":"Yuping Tang","orcid":"https://orcid.org/0000-0002-6581-3307"},"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":"Y. F. Tang","raw_affiliation_strings":["LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, People's Republic of China","School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, People's Republic of 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, People's Republic of China","institution_ids":["https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5103726418"],"corresponding_institution_ids":["https://openalex.org/I903994226"],"apc_list":null,"apc_paid":null,"fwci":0.3068,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.52301546,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"97","issue":"8","first_page":"1621","last_page":"1635"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9958000183105469,"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/superconvergence","display_name":"Superconvergence","score":0.8569054007530212},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.803970992565155},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.678059458732605},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5657802820205688},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5521178245544434},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5376300811767578},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5368236899375916},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49762848019599915},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.47628751397132874},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.4420197010040283},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4143974781036377},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22969093918800354},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09910708665847778}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.8569054007530212},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.803970992565155},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.678059458732605},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5657802820205688},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5521178245544434},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5376300811767578},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5368236899375916},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49762848019599915},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.47628751397132874},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.4420197010040283},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4143974781036377},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22969093918800354},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09910708665847778},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"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/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2019.1639676","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2019.1639676","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/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/G3267929876","display_name":"\u590d\u6742\u8154\u4f53\u4e0a\u7535\u78c1\u6563\u5c04\u5927\u6ce2\u6570\u95ee\u9898\u975e\u534f\u8c03\u5143\u903c\u8fd1\u53ca\u52a0\u901f\u6280\u672f\u7814\u7a76","funder_award_id":"11471296","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5651893690","display_name":null,"funder_award_id":"17A110011","funder_id":"https://openalex.org/F4320322878","funder_display_name":"Henan University"},{"id":"https://openalex.org/G6218630801","display_name":null,"funder_award_id":"19B110013","funder_id":"https://openalex.org/F4320322878","funder_display_name":"Henan University"},{"id":"https://openalex.org/G8653448250","display_name":null,"funder_award_id":"19HASTIT025","funder_id":"https://openalex.org/F4320322878","funder_display_name":"Henan University"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322878","display_name":"Henan University","ror":"https://ror.org/003xyzq10"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W162714136","https://openalex.org/W283099211","https://openalex.org/W582587363","https://openalex.org/W1964728661","https://openalex.org/W1967200406","https://openalex.org/W1973950856","https://openalex.org/W1980154613","https://openalex.org/W1986713454","https://openalex.org/W2000251948","https://openalex.org/W2001509015","https://openalex.org/W2006043132","https://openalex.org/W2008119119","https://openalex.org/W2014316843","https://openalex.org/W2015260916","https://openalex.org/W2016443018","https://openalex.org/W2025125818","https://openalex.org/W2027205768","https://openalex.org/W2051245043","https://openalex.org/W2066060749","https://openalex.org/W2077037251","https://openalex.org/W2085848537","https://openalex.org/W2088826361","https://openalex.org/W2090231693","https://openalex.org/W2123103679","https://openalex.org/W2129161483","https://openalex.org/W2138897104","https://openalex.org/W2185747134","https://openalex.org/W2256040747","https://openalex.org/W2267852856","https://openalex.org/W2275127356","https://openalex.org/W2282781400","https://openalex.org/W2295230376","https://openalex.org/W2299470766","https://openalex.org/W2397817385","https://openalex.org/W2515818747","https://openalex.org/W2516549324","https://openalex.org/W2526613690","https://openalex.org/W2560003211","https://openalex.org/W2589697132","https://openalex.org/W2753466262","https://openalex.org/W2754735025","https://openalex.org/W2766456430","https://openalex.org/W2769466798","https://openalex.org/W2791709173","https://openalex.org/W2793924997","https://openalex.org/W2799781908","https://openalex.org/W2799821673","https://openalex.org/W2803286947","https://openalex.org/W2870487173","https://openalex.org/W2963005592","https://openalex.org/W3098295690","https://openalex.org/W3099720254"],"related_works":["https://openalex.org/W2291214609","https://openalex.org/W3183609115","https://openalex.org/W2985206855","https://openalex.org/W2387056800","https://openalex.org/W2389908107","https://openalex.org/W2108850688","https://openalex.org/W2354295809","https://openalex.org/W2532653122","https://openalex.org/W2359833404","https://openalex.org/W2378343395"],"abstract_inverted_index":{"The":[0,44,111],"goal":[1],"of":[2,11,53,107],"this":[3],"paper":[4],"is":[5,46,65,78,96,103,120],"to":[6,57,71],"discuss":[7],"high":[8],"accuracy":[9],"analysis":[10,52],"a":[12,74],"fully-discrete":[13],"scheme":[14],"for":[15,62],"2D":[16],"multi-term":[17],"time":[18,40],"fractional":[19],"wave":[20],"equations":[21],"with":[22,59],"variable":[23,63],"coefficient":[24,64],"on":[25],"anisotropic":[26],"meshes":[27],"by":[28,32,41,105],"approximating":[29],"in":[30,39],"space":[31],"linear":[33,92],"triangular":[34,93],"finite":[35,94],"element":[36,95],"method":[37,119],"and":[38,80,88,123],"Crank-Nicolson":[42],"scheme.":[43],"stability":[45],"firstly":[47],"proved":[48],"unconditionally.":[49],"In":[50,69],"the":[51,60,66,81,84,99,116],"superclose":[54],"properties,":[55],"how":[56],"deal":[58],"item":[61],"main":[67],"difficulty.":[68],"order":[70],"do":[72],"this,":[73],"new":[75],"projection":[76,86],"operator":[77,87,90],"defined":[79],"relationship":[82],"between":[83],"proposed":[85,117],"interpolation":[89,108],"about":[91],"deduced.":[97],"Consequently,":[98],"global":[100],"superconvergence":[101],"result":[102],"obtained":[104],"use":[106],"postprocessing":[109],"technique.":[110],"numerical":[112,118],"examples":[113],"show":[114],"that":[115],"highly":[121],"accurate":[122],"computationally":[124],"efficient.":[125]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
