{"id":"https://openalex.org/W4414403863","doi":"https://doi.org/10.1007/s10915-025-03056-z","title":"Supercloseness of the HDG Method on Shishkin Mesh for a Singularly Perturbed Convection Diffusion Problem in 2D","display_name":"Supercloseness of the HDG Method on Shishkin Mesh for a Singularly Perturbed Convection Diffusion Problem in 2D","publication_year":2025,"publication_date":"2025-09-22","ids":{"openalex":"https://openalex.org/W4414403863","doi":"https://doi.org/10.1007/s10915-025-03056-z"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-025-03056-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-025-03056-z","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"Journal of Scientific Computing","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/A5072317766","display_name":"Xiaoqi Ma","orcid":"https://orcid.org/0000-0002-5565-092X"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaoqi Ma","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China"],"raw_orcid":"https://orcid.org/0000-0002-5565-092X","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China","institution_ids":["https://openalex.org/I28006308"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100782823","display_name":"Jin Zhang","orcid":"https://orcid.org/0009-0008-7695-1415"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jin Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China","institution_ids":["https://openalex.org/I28006308"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5072317766"],"corresponding_institution_ids":["https://openalex.org/I28006308"],"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":0.36273453,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"105","issue":"2","first_page":null,"last_page":null},"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":0.9994999766349792,"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":0.996399998664856,"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/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7505000233650208},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6021999716758728},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.5340999960899353},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.48010000586509705},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.47870001196861267},{"id":"https://openalex.org/keywords/superconvergence","display_name":"Superconvergence","score":0.4657000005245209},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4537000060081482},{"id":"https://openalex.org/keywords/convection","display_name":"Convection","score":0.4357999861240387}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.863099992275238},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7505000233650208},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6021999716758728},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5418999791145325},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.5340999960899353},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.48010000586509705},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.47870001196861267},{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.4657000005245209},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4537000060081482},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.4357999861240387},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43299999833106995},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.4032000005245209},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3977999985218048},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.38659998774528503},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3788999915122986},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.36059999465942383},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.35109999775886536},{"id":"https://openalex.org/C2989268449","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Energy method","level":2,"score":0.3434999883174896},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3001999855041504},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.27489998936653137},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2599000036716461},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.25380000472068787}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-025-03056-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-025-03056-z","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"Journal of Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2272832679","display_name":null,"funder_award_id":"11771257","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":33,"referenced_works":["https://openalex.org/W1978682560","https://openalex.org/W1985859449","https://openalex.org/W1993443533","https://openalex.org/W1998894128","https://openalex.org/W2009874724","https://openalex.org/W2012938047","https://openalex.org/W2022741557","https://openalex.org/W2027456895","https://openalex.org/W2030085198","https://openalex.org/W2061359862","https://openalex.org/W2073432708","https://openalex.org/W2074769980","https://openalex.org/W2095524611","https://openalex.org/W2099888904","https://openalex.org/W2100295905","https://openalex.org/W2110320615","https://openalex.org/W2147584861","https://openalex.org/W2149374694","https://openalex.org/W2260146335","https://openalex.org/W2460533716","https://openalex.org/W2472513481","https://openalex.org/W2528265074","https://openalex.org/W2805001116","https://openalex.org/W2901393796","https://openalex.org/W2963877237","https://openalex.org/W2964181612","https://openalex.org/W2983972779","https://openalex.org/W3130282808","https://openalex.org/W4205634890","https://openalex.org/W4239837487","https://openalex.org/W4241946322","https://openalex.org/W4324355356","https://openalex.org/W4367299042"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}