{"id":"https://openalex.org/W4223614005","doi":"https://doi.org/10.1007/s11075-022-01300-3","title":"A hybridizable discontinuous triangular spectral element method on unstructured meshes and its hp-error estimates","display_name":"A hybridizable discontinuous triangular spectral element method on unstructured meshes and its hp-error estimates","publication_year":2022,"publication_date":"2022-04-12","ids":{"openalex":"https://openalex.org/W4223614005","doi":"https://doi.org/10.1007/s11075-022-01300-3"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-022-01300-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-022-01300-3","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/A5071546038","display_name":"Bingzhen Zhou","orcid":null},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bingzhen Zhou","raw_affiliation_strings":["Key Laboratory of Computing and Stochastic Mathematics, Ministry of Education (LCSM), College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081, People\u2019s Republic of China","Key Laboratory of Computing and Stochastic Mathematics, Ministry of Education (LCSM), College of Mathematics and Computer Science, Hunan Normal University, Changsha, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Computing and Stochastic Mathematics, Ministry of Education (LCSM), College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081, People\u2019s Republic of China","institution_ids":["https://openalex.org/I173759888"]},{"raw_affiliation_string":"Key Laboratory of Computing and Stochastic Mathematics, Ministry of Education (LCSM), College of Mathematics and Computer Science, Hunan Normal University, Changsha, People\u2019s Republic of China","institution_ids":["https://openalex.org/I173759888"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069280334","display_name":"Bo Wang","orcid":"https://orcid.org/0000-0002-2748-1073"},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bo Wang","raw_affiliation_strings":["Key Laboratory of Computing and Stochastic Mathematics, Ministry of Education (LCSM), College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081, People\u2019s Republic of China","Key Laboratory of Computing and Stochastic Mathematics, Ministry of Education (LCSM), College of Mathematics and Computer Science, Hunan Normal University, Changsha, People\u2019s Republic of China"],"raw_orcid":"https://orcid.org/0000-0002-2748-1073","affiliations":[{"raw_affiliation_string":"Key Laboratory of Computing and Stochastic Mathematics, Ministry of Education (LCSM), College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081, People\u2019s Republic of China","institution_ids":["https://openalex.org/I173759888"]},{"raw_affiliation_string":"Key Laboratory of Computing and Stochastic Mathematics, Ministry of Education (LCSM), College of Mathematics and Computer Science, Hunan Normal University, Changsha, People\u2019s Republic of China","institution_ids":["https://openalex.org/I173759888"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112395743","display_name":"Li-Lian Wang","orcid":"https://orcid.org/0000-0002-2735-9019"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Li-Lian Wang","raw_affiliation_strings":["Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore","Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110405587","display_name":"Ziqing Xie","orcid":"https://orcid.org/0000-0001-9372-7011"},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ziqing Xie","raw_affiliation_strings":["Key Laboratory of Computing and Stochastic Mathematics, Ministry of Education (LCSM), College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081, People\u2019s Republic of China","Key Laboratory of Computing and Stochastic Mathematics, Ministry of Education (LCSM), College of Mathematics and Computer Science, Hunan Normal University, Changsha, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Computing and Stochastic Mathematics, Ministry of Education (LCSM), College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081, People\u2019s Republic of China","institution_ids":["https://openalex.org/I173759888"]},{"raw_affiliation_string":"Key Laboratory of Computing and Stochastic Mathematics, Ministry of Education (LCSM), College of Mathematics and Computer Science, Hunan Normal University, Changsha, People\u2019s Republic of China","institution_ids":["https://openalex.org/I173759888"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5069280334"],"corresponding_institution_ids":["https://openalex.org/I173759888"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03029752,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"91","issue":"3","first_page":"1231","last_page":"1260"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.8676983714103699},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.8464774489402771},{"id":"https://openalex.org/keywords/rectangle","display_name":"Rectangle","score":0.6028183102607727},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6022173762321472},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.5478236675262451},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5340643525123596},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5330435633659363},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.48964864015579224},{"id":"https://openalex.org/keywords/flexibility","display_name":"Flexibility (engineering)","score":0.47594523429870605},{"id":"https://openalex.org/keywords/spectral-element-method","display_name":"Spectral element method","score":0.4552331268787384},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.41376930475234985},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3805087208747864},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2906750440597534},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2710506021976471},{"id":"https://openalex.org/keywords/extended-finite-element-method","display_name":"Extended finite element method","score":0.1633438766002655},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06611824035644531}],"concepts":[{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.8676983714103699},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.8464774489402771},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.6028183102607727},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6022173762321472},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.5478236675262451},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5340643525123596},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5330435633659363},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.48964864015579224},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.47594523429870605},{"id":"https://openalex.org/C38961997","wikidata":"https://www.wikidata.org/wiki/Q7575186","display_name":"Spectral element method","level":4,"score":0.4552331268787384},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.41376930475234985},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3805087208747864},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2906750440597534},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2710506021976471},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.1633438766002655},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06611824035644531},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-022-01300-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-022-01300-3","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":[{"score":0.41999998688697815,"id":"https://metadata.un.org/sdg/13","display_name":"Climate action"}],"awards":[{"id":"https://openalex.org/G1668082357","display_name":null,"funder_award_id":"12022104","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1759577591","display_name":"\u4e09\u89d2\u5f62/\u56db\u9762\u4f53\u6742\u4ea4\u95f4\u65ad\u8c31\u5143\u6cd5\u53ca\u5176\u9884\u5904\u7406\u5b50\u7814\u7a76","funder_award_id":"11771137","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G442931909","display_name":null,"funder_award_id":"MOE2018-T2-1-059","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"},{"id":"https://openalex.org/G4916733487","display_name":"\u8ba1\u7b97\u975e\u51f8\u95ee\u9898\u978d\u70b9\u7684\u65b0\u7b97\u6cd5\u53ca\u5176\u5e94\u7528\u7814\u7a76","funder_award_id":"11771138","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5146864000","display_name":null,"funder_award_id":"MOE2017-T2-2-144","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"},{"id":"https://openalex.org/G7973434593","display_name":null,"funder_award_id":"CX20190337","funder_id":"https://openalex.org/F4320326217","funder_display_name":"Hunan Provincial Innovation Foundation for Postgraduate"}],"funders":[{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320326217","display_name":"Hunan Provincial Innovation Foundation for Postgraduate","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W321261355","https://openalex.org/W1570370571","https://openalex.org/W1627568958","https://openalex.org/W1976584147","https://openalex.org/W1998894128","https://openalex.org/W2003696205","https://openalex.org/W2028680761","https://openalex.org/W2030085198","https://openalex.org/W2040787464","https://openalex.org/W2041640855","https://openalex.org/W2047352485","https://openalex.org/W2068679290","https://openalex.org/W2069847349","https://openalex.org/W2081163355","https://openalex.org/W2082741499","https://openalex.org/W2084565106","https://openalex.org/W2091354775","https://openalex.org/W2118468229","https://openalex.org/W2127570421","https://openalex.org/W2149374694","https://openalex.org/W2155131245","https://openalex.org/W2237322020","https://openalex.org/W2267881438","https://openalex.org/W2329077087","https://openalex.org/W2376378314","https://openalex.org/W2405687382","https://openalex.org/W2915947382","https://openalex.org/W4205634890","https://openalex.org/W4239114676","https://openalex.org/W4251197584","https://openalex.org/W4256055182","https://openalex.org/W6600529467"],"related_works":["https://openalex.org/W2242098268","https://openalex.org/W4244945894","https://openalex.org/W4295815745","https://openalex.org/W2953079798","https://openalex.org/W1969674427","https://openalex.org/W3092754077","https://openalex.org/W2577524440","https://openalex.org/W2082439714","https://openalex.org/W2057146718","https://openalex.org/W2796540435"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}