{"id":"https://openalex.org/W1887008174","doi":"https://doi.org/10.1090/mcom/3186","title":"Hessian recovery for finite element methods","display_name":"Hessian recovery for finite element methods","publication_year":2016,"publication_date":"2016-06-08","ids":{"openalex":"https://openalex.org/W1887008174","doi":"https://doi.org/10.1090/mcom/3186","mag":"1887008174"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3186","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3186","pdf_url":"https://www.ams.org/mcom/2017-86-306/S0025-5718-2016-03186-5/S0025-5718-2016-03186-5.pdf","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":null,"license_id":null,"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":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2017-86-306/S0025-5718-2016-03186-5/S0025-5718-2016-03186-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044223666","display_name":"Hailong Guo","orcid":"https://orcid.org/0000-0001-7621-2315"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]},{"id":"https://openalex.org/I185443292","display_name":"Wayne State University","ror":"https://ror.org/01070mq45","country_code":"US","type":"education","lineage":["https://openalex.org/I185443292"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hailong Guo","raw_affiliation_strings":["Department of Mathematics, University of California, Santa Barbara, California 93106","Department of Mathematics, Wayne State University, Detroit, Michigan 48202"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Santa Barbara, California 93106","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Department of Mathematics, Wayne State University, Detroit, Michigan 48202","institution_ids":["https://openalex.org/I185443292"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100406520","display_name":"Zhimin Zhang","orcid":"https://orcid.org/0000-0002-0531-9112"},"institutions":[{"id":"https://openalex.org/I185443292","display_name":"Wayne State University","ror":"https://ror.org/01070mq45","country_code":"US","type":"education","lineage":["https://openalex.org/I185443292"]},{"id":"https://openalex.org/I4210139958","display_name":"Beijing Computational Science Research Center","ror":"https://ror.org/04tavf782","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139958"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Zhimin Zhang","raw_affiliation_strings":["Beijing Computational Science Research Center, Beijing 100193, China \u00e2\u0080\u0093 and \u00e2\u0080\u0093 Department of Mathematics, Wayne State University, Detroit, Michigan 48202","Beijing Computational Science Research Center, Beijing 100193, China \u2013 and \u2013 Department of Mathematics, Wayne State University, Detroit, Michigan 48202"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Computational Science Research Center, Beijing 100193, China \u00e2\u0080\u0093 and \u00e2\u0080\u0093 Department of Mathematics, Wayne State University, Detroit, Michigan 48202","institution_ids":["https://openalex.org/I185443292"]},{"raw_affiliation_string":"Beijing Computational Science Research Center, Beijing 100193, China \u2013 and \u2013 Department of Mathematics, Wayne State University, Detroit, Michigan 48202","institution_ids":["https://openalex.org/I185443292","https://openalex.org/I4210139958"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100750475","display_name":"Ren Zhao","orcid":"https://orcid.org/0000-0002-2896-4093"},"institutions":[{"id":"https://openalex.org/I185443292","display_name":"Wayne State University","ror":"https://ror.org/01070mq45","country_code":"US","type":"education","lineage":["https://openalex.org/I185443292"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ren Zhao","raw_affiliation_strings":["Department of Mathematics, Wayne State University, Detroit, Michigan 48202","Department of Mathematics , Wayne State University , Detroit, Michigan, 48202"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Wayne State University, Detroit, Michigan 48202","institution_ids":["https://openalex.org/I185443292"]},{"raw_affiliation_string":"Department of Mathematics , Wayne State University , Detroit, Michigan, 48202","institution_ids":["https://openalex.org/I185443292"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3994,"has_fulltext":true,"cited_by_count":27,"citation_normalized_percentile":{"value":0.86060606,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"86","issue":"306","first_page":"1671","last_page":"1692"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9965999722480774,"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":0.9962999820709229,"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/hessian-matrix","display_name":"Hessian matrix","score":0.9139732122421265},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8133277893066406},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7720479965209961},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.7627453804016113},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5144631862640381},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5121753215789795},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.44971713423728943},{"id":"https://openalex.org/keywords/hessian-equation","display_name":"Hessian equation","score":0.4316803514957428},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.417098730802536},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34204915165901184},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15482136607170105},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.11553493142127991},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.050508975982666016}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.9139732122421265},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8133277893066406},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7720479965209961},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.7627453804016113},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5144631862640381},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5121753215789795},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.44971713423728943},{"id":"https://openalex.org/C73729460","wikidata":"https://www.wikidata.org/wiki/Q17023339","display_name":"Hessian equation","level":4,"score":0.4316803514957428},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.417098730802536},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34204915165901184},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15482136607170105},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.11553493142127991},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.050508975982666016},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/mcom/3186","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3186","pdf_url":"https://www.ams.org/mcom/2017-86-306/S0025-5718-2016-03186-5/S0025-5718-2016-03186-5.pdf","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.747.1272","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.747.1272","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1406.3108.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/mcom/3186","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3186","pdf_url":"https://www.ams.org/mcom/2017-86-306/S0025-5718-2016-03186-5/S0025-5718-2016-03186-5.pdf","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2191606095","display_name":null,"funder_award_id":"DMS-1419040","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2660812258","display_name":null,"funder_award_id":"11471031","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2746842099","display_name":null,"funder_award_id":"91430216","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3715460442","display_name":null,"funder_award_id":"DMS-1419040","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4472046779","display_name":"\u82e5\u5e72\u5177\u6709\u5f31\u5bfc\u6570\u7684\u65b0\u578b\u8ba1\u7b97\u65b9\u6cd5\u7684\u68af\u5ea6\u91cd\u6784","funder_award_id":"11471031","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8598914340","display_name":null,"funder_award_id":"91430216","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1887008174.pdf","grobid_xml":"https://content.openalex.org/works/W1887008174.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1595515622","https://openalex.org/W1630432117","https://openalex.org/W1855169650","https://openalex.org/W2001012793","https://openalex.org/W2003049157","https://openalex.org/W2022244886","https://openalex.org/W2037685118","https://openalex.org/W2039914256","https://openalex.org/W2041523977","https://openalex.org/W2041731822","https://openalex.org/W2042199582","https://openalex.org/W2042502904","https://openalex.org/W2044892973","https://openalex.org/W2050178911","https://openalex.org/W2055009689","https://openalex.org/W2065479689","https://openalex.org/W2066488364","https://openalex.org/W2073821379","https://openalex.org/W2078897669","https://openalex.org/W2087271632","https://openalex.org/W2101577814","https://openalex.org/W2117905233","https://openalex.org/W2255584302","https://openalex.org/W3021722416","https://openalex.org/W3103371441","https://openalex.org/W3103648785","https://openalex.org/W3204708751"],"related_works":["https://openalex.org/W1991833659","https://openalex.org/W2316166864","https://openalex.org/W2964019050","https://openalex.org/W2989823969","https://openalex.org/W4286909496","https://openalex.org/W2890919253","https://openalex.org/W2414981476","https://openalex.org/W4297791817","https://openalex.org/W2755749970","https://openalex.org/W2120338570"],"abstract_inverted_index":{"In":[0,94],"this":[1],"article,":[2],"we":[3],"propose":[4],"and":[5,55],"analyze":[6],"an":[7],"effective":[8],"Hessian":[9,26],"recovery":[10,27],"strategy":[11],"for":[12,106],"the":[13,24,96,107],"Lagrangian":[14],"finite":[15,110],"element":[16,111],"method":[17,28,97],"of":[18,31,60,113],"arbitrary":[19],"order.":[20,115],"We":[21],"prove":[22],"that":[23],"proposed":[25],"preserves":[29],"polynomials":[30],"degree":[32],"<inline-formula":[33,61],"content-type=\"math/mathml\">":[34,62],"<mml:math":[35,63],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[36,64],"alttext=\"k":[37],"plus":[38],"1\">":[39],"<mml:semantics>":[40,73],"<mml:mrow>":[41,74],"<mml:mi>k</mml:mi>":[42,80],"<mml:mo>+</mml:mo>":[43],"<mml:mn>1</mml:mn>":[44],"</mml:mrow>":[45,84],"<mml:annotation":[46,85],"encoding=\"application/x-tex\">k+1</mml:annotation>":[47],"</mml:semantics>":[48,87],"</mml:math>":[49,88],"</inline-formula>":[50,89],"on":[51,90],"general":[52],"unstructured":[53],"meshes":[54],"superconverges":[56],"at":[57],"a":[58],"rate":[59],"alttext=\"upper":[65],"O":[66],"left-parenthesis":[67],"h":[68],"Superscript":[69],"k":[70],"Baseline":[71],"right-parenthesis\">":[72],"<mml:mi>O</mml:mi>":[75],"<mml:mo":[76,82],"stretchy=\"false\">(</mml:mo>":[77],"<mml:msup>":[78],"<mml:mi>h</mml:mi>":[79],"</mml:msup>":[81],"stretchy=\"false\">)</mml:mo>":[83],"encoding=\"application/x-tex\">O(h^k)</mml:annotation>":[86],"mildly":[91],"structured":[92],"meshes.":[93],"addition,":[95],"is":[98],"proved":[99],"to":[100,120],"be":[101],"ultraconvergent":[102],"(two":[103],"orders":[104],"higher)":[105],"translation":[108],"invariant":[109],"space":[112],"any":[114],"Numerical":[116],"examples":[117],"are":[118],"presented":[119],"support":[121],"our":[122],"theoretical":[123],"results.":[124]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
