{"id":"https://openalex.org/W2099213864","doi":"https://doi.org/10.1090/s0025-5718-2012-02610-x","title":"Local a posteriori error estimates for time-dependent Hamilton-Jacobi equations","display_name":"Local a posteriori error estimates for time-dependent Hamilton-Jacobi equations","publication_year":2012,"publication_date":"2012-06-05","ids":{"openalex":"https://openalex.org/W2099213864","doi":"https://doi.org/10.1090/s0025-5718-2012-02610-x","mag":"2099213864"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2012-02610-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02610-x","pdf_url":"https://www.ams.org/mcom/2013-82-281/S0025-5718-2012-02610-X/S0025-5718-2012-02610-X.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/2013-82-281/S0025-5718-2012-02610-X/S0025-5718-2012-02610-X.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091258269","display_name":"Bernardo Cockburn","orcid":"https://orcid.org/0000-0001-6085-3441"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bernardo Cockburn","raw_affiliation_strings":["School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, Minnesota 55455"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, Minnesota 55455","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018288017","display_name":"Ivan Merev","orcid":null},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ivan Merev","raw_affiliation_strings":["School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, Minnesota 55455"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, Minnesota 55455","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013248904","display_name":"Jianliang Qian","orcid":"https://orcid.org/0000-0003-3058-0096"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jianliang Qian","raw_affiliation_strings":["Department of Mathematics, Michigan State University, East Lansing, Michigan 48824"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Michigan State University, East Lansing, Michigan 48824","institution_ids":["https://openalex.org/I87216513"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.261,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.58270918,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"82","issue":"281","first_page":"187","last_page":"212"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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":0.9984999895095825,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8921682834625244},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.723208487033844},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.7196892499923706},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.540305495262146}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8921682834625244},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.723208487033844},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.7196892499923706},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.540305495262146},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-2012-02610-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02610-x","pdf_url":"https://www.ams.org/mcom/2013-82-281/S0025-5718-2012-02610-X/S0025-5718-2012-02610-X.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"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2012-02610-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02610-x","pdf_url":"https://www.ams.org/mcom/2013-82-281/S0025-5718-2012-02610-X/S0025-5718-2012-02610-X.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/G5893083292","display_name":"New numerical methods for Hamilton-Jacobi equations, Gaussian beams, and kinetic inverse problems","funder_award_id":"0810104","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8138177391","display_name":null,"funder_award_id":"DMS-0712955","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8147697595","display_name":"Gaussian Beam Methods for Large-Scale Computational Electromagnetics and Applications","funder_award_id":"0830161","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8884215749","display_name":"Discontinuous Galerkin Methods for Partial Differential Equations","funder_award_id":"0712955","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"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2099213864.pdf","grobid_xml":"https://content.openalex.org/works/W2099213864.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W153353184","https://openalex.org/W305332711","https://openalex.org/W1238092070","https://openalex.org/W1550828720","https://openalex.org/W1967289650","https://openalex.org/W1986788497","https://openalex.org/W1986838484","https://openalex.org/W1988044952","https://openalex.org/W1989067183","https://openalex.org/W1995720627","https://openalex.org/W1998857370","https://openalex.org/W2012999285","https://openalex.org/W2017747263","https://openalex.org/W2027438381","https://openalex.org/W2039802576","https://openalex.org/W2057462050","https://openalex.org/W2067187920","https://openalex.org/W2071602743","https://openalex.org/W2075869990","https://openalex.org/W2095148363","https://openalex.org/W2098432798","https://openalex.org/W2108193376","https://openalex.org/W2138175174","https://openalex.org/W2157153211","https://openalex.org/W2312018620","https://openalex.org/W2470369492","https://openalex.org/W2530190071","https://openalex.org/W2749408143","https://openalex.org/W3021722416","https://openalex.org/W4238016064","https://openalex.org/W4241127195","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4200506717","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W3137869026"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"obtain":[4],"the":[5,54,61,119,122,156,160,168,185,189,248,297,300],"first":[6],"local":[7],"a":[8,38,250,301],"posteriori":[9,251,267,302],"error":[10,158,236,252,268,303],"estimate":[11,55,215,253],"for":[12,60,217,230,238,270,274,285],"time-dependent":[13,239,280],"Hamilton-Jacobi":[14,240,275],"equations.":[15,241,276],"Given":[16],"an":[17,57,227,245],"arbitrary":[18],"domain":[19,161],"<inline-formula":[20,40,62,86,105,125,141,172,196],"content-type=\"math/mathml\">":[21,41,63,87,106,126,142,173,197],"<mml:math":[22,42,64,88,107,127,143,174,198],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[23,43,65,89,108,128,144,175,199],"alttext=\"normal":[24,90,200],"upper":[25,58,91,201],"Omega\">":[26,92,202],"<mml:semantics>":[27,46,71,93,111,130,146,177,203],"<mml:mi":[28,74,94,204],"mathvariant=\"normal\">":[29,75,95,205],"\u03a9":[30,96,206],"</mml:mi>":[31,77,97,207],"<mml:annotation":[32,48,79,98,113,132,148,179,208],"encoding=\"application/x-tex\">\\Omega</mml:annotation>":[33,99,209],"</mml:semantics>":[34,50,81,100,115,134,150,181,210],"</mml:math>":[35,51,82,101,116,135,151,182,211],"</inline-formula>":[36,52,83,102,117,136,152,183,212],"and":[37,137,164,220,262],"time":[39,104],"alttext=\"upper":[44,66,109],"T\">":[45,110],"<mml:mi>T</mml:mi>":[47,112],"encoding=\"application/x-tex\">T</mml:annotation>":[49,114],",":[53,282],"gives":[56],"bound":[59],"L":[67],"Superscript":[68],"normal":[69],"infinity\">":[70],"<mml:msup>":[72],"<mml:mi>L</mml:mi>":[73],"\u221e":[76],"</mml:msup>":[78],"encoding=\"application/x-tex\">L^\\infty</mml:annotation>":[80],"-norm":[84],"in":[85,153,159,165,184,195,265],"at":[103],"of":[118,155,162,167,171,187,191,299],"difference":[120],"between":[121],"viscosity":[123],"solution":[124],"alttext=\"u\">":[129],"<mml:mi>u</mml:mi>":[131],"encoding=\"application/x-tex\">u</mml:annotation>":[133],"any":[138,221],"continuous":[139],"function":[140],"alttext=\"v\">":[145,176],"<mml:mi>v</mml:mi>":[147,178],"encoding=\"application/x-tex\">v</mml:annotation>":[149,180],"terms":[154,166],"initial":[157],"dependence":[163,192],"(shifted)":[169],"residual":[170],"union":[186],"all":[188],"cones":[190],"with":[193,234],"vertices":[194],".":[213],"The":[214,279],"holds":[216],"general":[218,271],"Hamiltonians":[219],"space":[222],"dimension.":[223],"It":[224],"is":[225,244],"thus":[226],"ideal":[228],"tool":[229],"devising":[231],"adaptive":[232],"algorithms":[233],"rigorous":[235],"control":[237],"This":[242],"result":[243],"extension":[246],"to":[247],"global":[249],"obtained":[254],"by":[255],"S.":[256],"Albert,":[257],"B.":[258],"Cockburn,":[259],"D.":[260],"French,":[261],"T.":[263],"Peterson":[264],"<italic>A":[266],"estimates":[269,304],"numerical":[272],"methods":[273],"Part":[277],"II:":[278],"case</italic>":[281],"Finite":[283],"Volumes":[284],"Complex":[286],"Applications,":[287],"vol.":[288],"III,":[289],"June":[290],"2002,":[291],"pp.":[292],"17\u201324.":[293],"Numerical":[294],"experiments":[295],"investigating":[296],"sharpness":[298],"are":[305],"given.":[306]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
