{"id":"https://openalex.org/W2022599090","doi":"https://doi.org/10.1137/05063756x","title":"The Optimal Convergence of the<i>h</i>\u2010<i>p</i>Version of the Finite Element Method with Quasi\u2010Uniform Meshes","display_name":"The Optimal Convergence of the<i>h</i>\u2010<i>p</i>Version of the Finite Element Method with Quasi\u2010Uniform Meshes","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2022599090","doi":"https://doi.org/10.1137/05063756x","mag":"2022599090"},"language":"en","primary_location":{"id":"doi:10.1137/05063756x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/05063756x","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://scholars.cityu.edu.hk/en/publications/the-optimal-convergence-of-the-h-p-version-of-the-finite-element-","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100885624","display_name":"Benqi Guo","orcid":null},"institutions":[{"id":"https://openalex.org/I46247651","display_name":"University of Manitoba","ror":"https://ror.org/02gfys938","country_code":"CA","type":"education","lineage":["https://openalex.org/I46247651"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Benqi Guo","raw_affiliation_strings":["University of Manitoba"],"affiliations":[{"raw_affiliation_string":"University of Manitoba","institution_ids":["https://openalex.org/I46247651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014226512","display_name":"Weiwei Sun","orcid":"https://orcid.org/0000-0002-2079-4480"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Weiwei Sun","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100885624"],"corresponding_institution_ids":["https://openalex.org/I46247651"],"apc_list":null,"apc_paid":null,"fwci":3.0001,"has_fulltext":true,"cited_by_count":33,"citation_normalized_percentile":{"value":0.90143975,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"45","issue":"2","first_page":"698","last_page":"730"},"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":0.9995999932289124,"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":0.9995999932289124,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.996999979019165,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.995199978351593,"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/polygon-mesh","display_name":"Polygon mesh","score":0.943150520324707},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8079741597175598},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7705123424530029},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7074931263923645},{"id":"https://openalex.org/keywords/uniform-convergence","display_name":"Uniform convergence","score":0.5603545904159546},{"id":"https://openalex.org/keywords/volume-mesh","display_name":"Volume mesh","score":0.5011405944824219},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.441731333732605},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4390057325363159},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.41035863757133484},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.325683057308197},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.30455711483955383},{"id":"https://openalex.org/keywords/mesh-generation","display_name":"Mesh generation","score":0.21077439188957214},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10689517855644226}],"concepts":[{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.943150520324707},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8079741597175598},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7705123424530029},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7074931263923645},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.5603545904159546},{"id":"https://openalex.org/C170589453","wikidata":"https://www.wikidata.org/wiki/Q7940896","display_name":"Volume mesh","level":4,"score":0.5011405944824219},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.441731333732605},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4390057325363159},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.41035863757133484},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.325683057308197},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.30455711483955383},{"id":"https://openalex.org/C181145010","wikidata":"https://www.wikidata.org/wiki/Q4418033","display_name":"Mesh generation","level":3,"score":0.21077439188957214},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10689517855644226},{"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},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/05063756x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/05063756x","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/the-optimal-convergence-of-the-h-p-version-of-the-finite-element-","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/5ed28a03-bb1b-4f1c-b3ef-e050b8ef550e","is_oa":true,"landing_page_url":"https://hdl.handle.net/2031/5ed28a03-bb1b-4f1c-b3ef-e050b8ef550e","pdf_url":"https://scholars.cityu.edu.hk/files/189032353/5281260.pdf","source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Guo, B & Sun, W 2007, 'The optimal convergence of the h-p version of the finite element method with quasi-uniform meshes', SIAM Journal on Numerical Analysis, vol. 45, no. 2, pp. 698-730. https://doi.org/10.1137/05063756X","raw_type":"article"}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/the-optimal-convergence-of-the-h-p-version-of-the-finite-element-","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G113560337","display_name":null,"funder_award_id":"E03004","funder_id":"https://openalex.org/F4320334955","funder_display_name":"E-Institutes of Shanghai Municipal Education Commission"},{"id":"https://openalex.org/G7596950192","display_name":null,"funder_award_id":"E03004","funder_id":"https://openalex.org/F4320321881","funder_display_name":"Shanghai Municipal Education Commission"}],"funders":[{"id":"https://openalex.org/F4320309893","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23"},{"id":"https://openalex.org/F4320321881","display_name":"Shanghai Municipal Education Commission","ror":"https://ror.org/05tewj457"},{"id":"https://openalex.org/F4320322374","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320334955","display_name":"E-Institutes of Shanghai Municipal Education Commission","ror":"https://ror.org/05tewj457"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1965314915","https://openalex.org/W1967203400","https://openalex.org/W1971742591","https://openalex.org/W1973213510","https://openalex.org/W1982954693","https://openalex.org/W1983731610","https://openalex.org/W1999400032","https://openalex.org/W2000292231","https://openalex.org/W2015804955","https://openalex.org/W2017437995","https://openalex.org/W2040771049","https://openalex.org/W2045737730","https://openalex.org/W2056040698","https://openalex.org/W2068305880","https://openalex.org/W2072744569","https://openalex.org/W2080830307","https://openalex.org/W2082741499","https://openalex.org/W2094695561","https://openalex.org/W2108087611","https://openalex.org/W2120062331","https://openalex.org/W2126897161","https://openalex.org/W2133964250","https://openalex.org/W2146686865","https://openalex.org/W2170046081","https://openalex.org/W2307113332","https://openalex.org/W2490297076","https://openalex.org/W2525823748","https://openalex.org/W2792013640"],"related_works":["https://openalex.org/W2017968036","https://openalex.org/W2752501457","https://openalex.org/W1601688333","https://openalex.org/W2171421712","https://openalex.org/W2187005362","https://openalex.org/W1995603760","https://openalex.org/W2387220787","https://openalex.org/W3106617480","https://openalex.org/W4221158809","https://openalex.org/W4294653043"],"abstract_inverted_index":{"In":[0],"the":[1,4,10,13,24,53,57,61,77,81,87],"framework":[2],"of":[3,12,16,29,56,60],"Jacobi\u2010weighted":[5],"Besov":[6],"spaces,":[7],"we":[8],"analyze":[9],"convergence":[11,55],"h\u2010p":[14,58,78],"version":[15,59,79],"finite":[17,62],"element":[18,63],"solutions":[19],"on":[20,34,71],"quasi\u2010uniform":[21,66,84,90],"meshes":[22,67,85],"and":[23,26,38,48,86],"lower":[25,37],"upper":[27,39],"bounds":[28,40],"errors":[30],"for":[31,68,76],"elliptic":[32,69],"problems":[33,70],"polygons.":[35,72],"Both":[36],"are":[41],"proved":[42,75],"to":[43,52],"be":[44],"optimal":[45,54],"in":[46],"h":[47],"p,":[49],"which":[50],"leads":[51],"method":[64],"with":[65,83,89],"The":[73],"results":[74],"include":[80],"h\u2010version":[82],"p\u2010version":[88],"degrees":[91],"as":[92],"two":[93],"special":[94],"cases.":[95]},"counts_by_year":[{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-22T08:38:42.863108","created_date":"2025-10-10T00:00:00"}
