{"id":"https://openalex.org/W3066631337","doi":"https://doi.org/10.1007/s11075-020-00978-7","title":"A linearized high-order Galerkin finite element approach for two-dimensional nonlinear time fractional Klein-Gordon equations","display_name":"A linearized high-order Galerkin finite element approach for two-dimensional nonlinear time fractional Klein-Gordon equations","publication_year":2020,"publication_date":"2020-08-19","ids":{"openalex":"https://openalex.org/W3066631337","doi":"https://doi.org/10.1007/s11075-020-00978-7","mag":"3066631337"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-020-00978-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-020-00978-7","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","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/A5101981784","display_name":"Guoyu Zhang","orcid":"https://orcid.org/0000-0003-3977-5228"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guoyu Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100651262","display_name":"Chengming Huang","orcid":"https://orcid.org/0000-0001-8556-1111"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Chengming Huang","raw_affiliation_strings":["Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, China","School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China"],"raw_orcid":"https://orcid.org/0000-0001-8556-1111","affiliations":[{"raw_affiliation_string":"Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008145354","display_name":"Mingfa Fei","orcid":"https://orcid.org/0000-0001-7397-9342"},"institutions":[{"id":"https://openalex.org/I198357462","display_name":"Changsha University","ror":"https://ror.org/011d8sm39","country_code":"CN","type":"education","lineage":["https://openalex.org/I198357462"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mingfa Fei","raw_affiliation_strings":["School of Computer Engineering and Applied Mathematics, Changsha University, Changsha, 410022, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Engineering and Applied Mathematics, Changsha University, Changsha, 410022, China","institution_ids":["https://openalex.org/I198357462"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100332734","display_name":"Nan Wang","orcid":"https://orcid.org/0000-0002-1500-6726"},"institutions":[{"id":"https://openalex.org/I38877650","display_name":"Zhengzhou University","ror":"https://ror.org/04ypx8c21","country_code":"CN","type":"education","lineage":["https://openalex.org/I38877650"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Nan Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, China","institution_ids":["https://openalex.org/I38877650"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100651262"],"corresponding_institution_ids":["https://openalex.org/I47720641"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.1395,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.54039591,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"87","issue":"2","first_page":"551","last_page":"574"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"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":1.0,"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":0.9980999827384949,"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/T10514","display_name":"Numerical methods in engineering","score":0.996999979019165,"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/mathematics","display_name":"Mathematics","score":0.8390297889709473},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8257090449333191},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6571231484413147},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6555535197257996},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6386317014694214},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5822240710258484},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5440002083778381},{"id":"https://openalex.org/keywords/temporal-discretization","display_name":"Temporal discretization","score":0.5230306386947632},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5201535820960999},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.5152857303619385},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.45993995666503906},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42104285955429077},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.09078419208526611},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06780344247817993}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8390297889709473},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8257090449333191},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6571231484413147},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6555535197257996},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6386317014694214},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5822240710258484},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5440002083778381},{"id":"https://openalex.org/C2778327290","wikidata":"https://www.wikidata.org/wiki/Q17146496","display_name":"Temporal discretization","level":3,"score":0.5230306386947632},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5201535820960999},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5152857303619385},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.45993995666503906},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42104285955429077},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09078419208526611},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06780344247817993},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"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:10.1007/s11075-020-00978-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-020-00978-7","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1863654007","display_name":null,"funder_award_id":"11771163","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":37,"referenced_works":["https://openalex.org/W374977727","https://openalex.org/W1526921167","https://openalex.org/W1964804260","https://openalex.org/W1969312973","https://openalex.org/W1973950856","https://openalex.org/W1988087043","https://openalex.org/W1988322580","https://openalex.org/W1990829983","https://openalex.org/W1993077381","https://openalex.org/W2017288915","https://openalex.org/W2047594597","https://openalex.org/W2054303016","https://openalex.org/W2059607966","https://openalex.org/W2065232540","https://openalex.org/W2081531908","https://openalex.org/W2081871678","https://openalex.org/W2082621526","https://openalex.org/W2083046996","https://openalex.org/W2091222631","https://openalex.org/W2104736025","https://openalex.org/W2343213775","https://openalex.org/W2345986302","https://openalex.org/W2467804905","https://openalex.org/W2516962718","https://openalex.org/W2577996109","https://openalex.org/W2580224004","https://openalex.org/W2604406592","https://openalex.org/W2619736124","https://openalex.org/W2740782266","https://openalex.org/W2782480706","https://openalex.org/W2792143917","https://openalex.org/W2800380917","https://openalex.org/W2806868147","https://openalex.org/W2907331802","https://openalex.org/W2954879421","https://openalex.org/W2991576200","https://openalex.org/W3101361006"],"related_works":["https://openalex.org/W2043686470","https://openalex.org/W2096756136","https://openalex.org/W2080994790","https://openalex.org/W2324487000","https://openalex.org/W4223973763","https://openalex.org/W2070144563","https://openalex.org/W1590663584","https://openalex.org/W2017533067","https://openalex.org/W2089783241","https://openalex.org/W3066631337"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":2}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}