{"id":"https://openalex.org/W2061287181","doi":"https://doi.org/10.1090/s0025-5718-2014-02810-x","title":"Linear finite element superconvergence on simplicial meshes","display_name":"Linear finite element superconvergence on simplicial meshes","publication_year":2014,"publication_date":"2014-02-12","ids":{"openalex":"https://openalex.org/W2061287181","doi":"https://doi.org/10.1090/s0025-5718-2014-02810-x","mag":"2061287181"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2014-02810-x","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2014-02810-x","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","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/A5100332995","display_name":"Jie Chen","orcid":"https://orcid.org/0000-0003-1036-007X"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Jie Chen","raw_affiliation_strings":["Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087806559","display_name":"Desheng Wang","orcid":null},"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":"Desheng Wang","raw_affiliation_strings":["Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056115552","display_name":"Qiang Du","orcid":"https://orcid.org/0000-0002-1067-8937"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qiang Du","raw_affiliation_strings":["Pennsylvania State University, University Park, Pennsylvania 16802","Pennsylvania State University, University  Park,  Pennsylvania   16802"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Pennsylvania State University, University Park, Pennsylvania 16802","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Pennsylvania State University, University  Park,  Pennsylvania   16802","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5594,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.81768724,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"83","issue":"289","first_page":"2161","last_page":"2185"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991999864578247,"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/superconvergence","display_name":"Superconvergence","score":0.965445876121521},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8293203711509705},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.8160753846168518},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7221785187721252},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.6416550278663635},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4865819215774536},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4862474203109741},{"id":"https://openalex.org/keywords/tetrahedron","display_name":"Tetrahedron","score":0.48594629764556885},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4603348672389984},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.4492380917072296},{"id":"https://openalex.org/keywords/volume-mesh","display_name":"Volume mesh","score":0.449209988117218},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.41986188292503357},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.41880717873573303},{"id":"https://openalex.org/keywords/mesh-generation","display_name":"Mesh generation","score":0.18103870749473572},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08677923679351807},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06408032774925232}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.965445876121521},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8293203711509705},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.8160753846168518},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7221785187721252},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.6416550278663635},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4865819215774536},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4862474203109741},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.48594629764556885},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4603348672389984},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4492380917072296},{"id":"https://openalex.org/C170589453","wikidata":"https://www.wikidata.org/wiki/Q7940896","display_name":"Volume mesh","level":4,"score":0.449209988117218},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.41986188292503357},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41880717873573303},{"id":"https://openalex.org/C181145010","wikidata":"https://www.wikidata.org/wiki/Q4418033","display_name":"Mesh generation","level":3,"score":0.18103870749473572},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08677923679351807},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06408032774925232},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-2014-02810-x","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2014-02810-x","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1494380125","https://openalex.org/W1543706572","https://openalex.org/W1582520000","https://openalex.org/W1975209811","https://openalex.org/W1980964769","https://openalex.org/W1989367394","https://openalex.org/W2005601391","https://openalex.org/W2030447403","https://openalex.org/W2039132604","https://openalex.org/W2042199582","https://openalex.org/W2044892973","https://openalex.org/W2050178911","https://openalex.org/W2051752778","https://openalex.org/W2053303770","https://openalex.org/W2055009689","https://openalex.org/W2065479689","https://openalex.org/W2069447707","https://openalex.org/W2108826765","https://openalex.org/W2131479138","https://openalex.org/W2135770948","https://openalex.org/W2142228262","https://openalex.org/W2155395549","https://openalex.org/W3093490726","https://openalex.org/W4230969472","https://openalex.org/W4254197176"],"related_works":["https://openalex.org/W2386448237","https://openalex.org/W2017968036","https://openalex.org/W2752501457","https://openalex.org/W4360891036","https://openalex.org/W1601688333","https://openalex.org/W2171421712","https://openalex.org/W2187005362","https://openalex.org/W1995603760","https://openalex.org/W2387220787","https://openalex.org/W2158103614"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,28,30,125,130,160,165,172,175,200,203,304,314,333],"linear":[3,176,204],"finite":[4,177],"element":[5,178],"gradient":[6,132,173,201],"superconvergence":[7],"on":[8,162],"special":[9,19],"simplicial":[10],"meshes":[11,312],"which":[12,157],"satisfy":[13],"an":[14,225],"edge":[15,315],"pair":[16,34,316],"condition.":[17],"This":[18],"geometric":[20],"condition":[21,161,317],"implies":[22],"that":[23,171,310,328],"for":[24,86,266],"most":[25],"simplexes":[26],"in":[27,38,141,322,335],"mesh,":[29],"lengths":[31],"of":[32,35,174,202],"each":[33,39],"opposite":[36],"edges":[37],"3-face":[40],"are":[41,300],"assumed":[42],"to":[43,199,302],"differ":[44],"only":[45],"by":[46],"<inline-formula":[47,89,112,143,180,206,227,267],"content-type=\"math/mathml\">":[48,90,113,144,181,207,228,268],"<mml:math":[49,91,114,145,182,208,229,269],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[50,92,115,146,183,209,230,270],"alttext=\"upper":[51,231],"O":[52,232],"left-parenthesis":[53,233],"h":[54,234],"Superscript":[55,235],"1":[56,236],"plus":[57,237],"alpha":[58],"Baseline":[59,239],"right-parenthesis\">":[60,240],"<mml:semantics>":[61,96,117,148,187,214,241,276],"<mml:mrow>":[62,97,242,277],"<mml:mi>O</mml:mi>":[63,243],"<mml:mo":[64,77,244,257],"stretchy=\"false\">(</mml:mo>":[65,245],"<mml:msup>":[66,246],"<mml:mi>h</mml:mi>":[67,118,190,247],"<mml:mrow":[68,248],"class=\"MJX-TeXAtom-ORD\">":[69,249],"<mml:mn>1</mml:mn>":[70,250],"<mml:mo>+</mml:mo>":[71,251],"<mml:mi>":[72,98,252,280,286],"\u03b1":[73,99,287],"</mml:mi>":[74,100,254,282,288],"</mml:mrow>":[75,79,103,255,259,289],"</mml:msup>":[76,256],"stretchy=\"false\">)</mml:mo>":[78,258],"<mml:annotation":[80,104,119,150,192,219,260,290],"encoding=\"application/x-tex\">O(h^{1+\\alpha":[81],"})</mml:annotation>":[82,262],"</mml:semantics>":[83,107,121,152,194,221,263,294],"</mml:math>":[84,108,122,153,195,222,264,295],"</inline-formula>":[85,109,123,154,196,223,265,296],"some":[87],"constant":[88],"alttext=\"alpha":[93],"greater-than":[94,272],"0\">":[95],"<mml:mo>&gt;</mml:mo>":[101,279],"<mml:mn>0</mml:mn>":[102,278],"encoding=\"application/x-tex\">\\alpha":[105],"&gt;0</mml:annotation>":[106],",":[110],"with":[111,224],"alttext=\"h\">":[116],"encoding=\"application/x-tex\">h</mml:annotation>":[120],"being":[124],"mesh":[126],"parameter.":[127],"To":[128],"analyze":[129],"interplant":[131],"superconvergence,":[133],"we":[134,169,308,325],"present":[135],"a":[136],"local":[137],"error":[138],"expansion":[139],"formula":[140],"general":[142],"alttext=\"n\">":[147],"<mml:mi>n</mml:mi>":[149],"encoding=\"application/x-tex\">n</mml:annotation>":[151],"dimensional":[155,167,337],"space":[156],"also":[158,326],"motivates":[159],"meshes.":[163],"In":[164],"three":[166,323],"space,":[168],"show":[170,327],"solution":[179],"alttext=\"u":[184,210],"Subscript":[185,211],"h\">":[186],"<mml:msub>":[188,215],"<mml:mi>u</mml:mi>":[189,216],"</mml:msub>":[191,218],"encoding=\"application/x-tex\">u_h</mml:annotation>":[193],"is":[197],"superconvergent":[198],"interpolatant":[205],"upper":[212],"I\">":[213],"<mml:mi>I</mml:mi>":[217],"encoding=\"application/x-tex\">u_I</mml:annotation>":[220],"order":[226],"rho":[238,273],"\u03c1":[253,281],"encoding=\"application/x-tex\">O(h^{1+\\rho":[261],"alttext=\"0":[271],"less-than-or-equal-to":[274],"alpha\">":[275],"<mml:mo>":[283],"\u2264":[284],"</mml:mo>":[285],"encoding=\"application/x-tex\">0&gt;\\rho":[291],"\\leq":[292],"\\alpha</mml:annotation>":[293],".":[297],"Numerical":[298],"examples":[299],"presented":[301],"verify":[303],"theoretical":[305],"findings.":[306],"While":[307],"illustrate":[309],"tetrahedral":[311],"satisfying":[313],"can":[318],"often":[319],"be":[320,332],"produced":[321],"dimension,":[324],"this":[329],"may":[330],"not":[331],"case":[334],"higher":[336],"spaces.":[338]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}