{"id":"https://openalex.org/W1986784896","doi":"https://doi.org/10.1090/s0025-5718-02-01464-3","title":"Enhanced accuracy by post-processing for finite element methods for hyperbolic equations","display_name":"Enhanced accuracy by post-processing for finite element methods for hyperbolic equations","publication_year":2002,"publication_date":"2002-11-20","ids":{"openalex":"https://openalex.org/W1986784896","doi":"https://doi.org/10.1090/s0025-5718-02-01464-3","mag":"1986784896"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-02-01464-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-02-01464-3","pdf_url":"https://www.ams.org/mcom/2003-72-242/S0025-5718-02-01464-3/S0025-5718-02-01464-3.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/2003-72-242/S0025-5718-02-01464-3/S0025-5718-02-01464-3.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, Minneapolis, Minnesota 55455","School of Mathematics, University of Minnesota, Minneapolis, Minnesota"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"School of Mathematics, University of Minnesota, Minneapolis, Minnesota","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036018970","display_name":"Mitchell Luskin","orcid":"https://orcid.org/0000-0003-1981-199X"},"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":"Mitchell Luskin","raw_affiliation_strings":["School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455","School of Mathematics, University of Minnesota, Minneapolis, Minnesota"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"School of Mathematics, University of Minnesota, Minneapolis, Minnesota","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047035333","display_name":"Chi\u2010Wang Shu","orcid":"https://orcid.org/0000-0001-7720-9564"},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chi-Wang Shu","raw_affiliation_strings":["Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912","Division of Applied Mathematics, Brown University, Providence, Rhode Island,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912","institution_ids":["https://openalex.org/I27804330"]},{"raw_affiliation_string":"Division of Applied Mathematics, Brown University, Providence, Rhode Island,","institution_ids":["https://openalex.org/I27804330"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064002486","display_name":"Endre S\u00fcli","orcid":"https://orcid.org/0000-0002-0812-6105"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Endre S\u00fcli","raw_affiliation_strings":["Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.6474,"has_fulltext":true,"cited_by_count":167,"citation_normalized_percentile":{"value":0.94461044,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"72","issue":"242","first_page":"577","last_page":"606"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9958999752998352,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.7221953868865967},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45810627937316895},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4213283658027649},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3904874324798584},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31430330872535706},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.1349996030330658}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7221953868865967},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45810627937316895},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4213283658027649},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3904874324798584},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31430330872535706},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.1349996030330658}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1090/s0025-5718-02-01464-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-02-01464-3","pdf_url":"https://www.ams.org/mcom/2003-72-242/S0025-5718-02-01464-3/S0025-5718-02-01464-3.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:uuid:ac729ea8-0ecd-4b45-9f18-a1ec288c718c","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"http://eprints.maths.ox.ac.uk/1248","raw_type":"Technical Report"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.103.125","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.103.125","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2003-72-242/S0025-5718-02-01464-3/S0025-5718-02-01464-3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.4457","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.4457","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/2003-72-242/S0025-5718-02-01464-3/S0025-5718-02-01464-3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.31.9018","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.9018","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://web.comlab.ox.ac.uk/oucl/work/endre.suli/postprocess.ps.gz","raw_type":"text"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:951dce16-2b9a-466e-897f-1e7d61ed8485","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:951dce16-2b9a-466e-897f-1e7d61ed8485","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements at Oxford","raw_type":"Journal article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:ac729ea8-0ecd-4b45-9f18-a1ec288c718c","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:ac729ea8-0ecd-4b45-9f18-a1ec288c718c","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprints.maths.ox.ac.uk/1248","raw_type":"Report"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-02-01464-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-02-01464-3","pdf_url":"https://www.ams.org/mcom/2003-72-242/S0025-5718-02-01464-3/S0025-5718-02-01464-3.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/G177218894","display_name":null,"funder_award_id":"F49620","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G3286829029","display_name":null,"funder_award_id":"DAAG55-97-1-0318","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/F4320306101","display_name":"National Aeronautics and Space Administration","ror":"https://ror.org/027ka1x80"},{"id":"https://openalex.org/F4320309636","display_name":"University of Minnesota","ror":"https://ror.org/03grvy078"},{"id":"https://openalex.org/F4320320875","display_name":"Deutscher Akademischer Austauschdienst","ror":"https://ror.org/039djdh30"},{"id":"https://openalex.org/F4320332378","display_name":"Langley Research Center","ror":"https://ror.org/0399mhs52"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1986784896.pdf","grobid_xml":"https://content.openalex.org/works/W1986784896.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W69785072","https://openalex.org/W70071832","https://openalex.org/W1535281435","https://openalex.org/W1538356049","https://openalex.org/W1595515622","https://openalex.org/W1596971969","https://openalex.org/W1676298003","https://openalex.org/W1963559825","https://openalex.org/W1976799546","https://openalex.org/W1987418883","https://openalex.org/W1996199419","https://openalex.org/W1999579808","https://openalex.org/W2003438645","https://openalex.org/W2007197813","https://openalex.org/W2008334472","https://openalex.org/W2012938047","https://openalex.org/W2016419036","https://openalex.org/W2018753322","https://openalex.org/W2019098734","https://openalex.org/W2065908448","https://openalex.org/W2079808083","https://openalex.org/W2092920123","https://openalex.org/W4232110500","https://openalex.org/W4237262710","https://openalex.org/W4243968994","https://openalex.org/W4246409132","https://openalex.org/W4252870981","https://openalex.org/W4253051628"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,37,44,50,53,64,111,117,123,155,175,203,236,239,337,345,348],"enhancement":[3],"of":[4,8,33,39,52,61,63,66,94,127,179,231,347],"accuracy,":[5],"by":[6],"means":[7],"a":[9,24,27,56,333],"simple":[10],"post-processing":[11,22],"technique,":[12],"for":[13,235],"finite":[14],"element":[15],"approximations":[16],"to":[17],"transient":[18],"hyperbolic":[19],"equations.":[20],"The":[21],"is":[23,46,55,120,126,178,206,233,332,340],"convolution":[25],"with":[26,243],"kernel":[28,54],"whose":[29,58],"support":[30,51],"has":[31],"measure":[32],"order":[34,65,128,180,230,244],"one":[35],"in":[36,110,154,207,226,270],"case":[38,228],"arbitrary":[40],"unstructured":[41],"meshes;":[42],"if":[43,202],"mesh":[45],"locally":[47],"translation":[48],"invariant,":[49],"cube":[57],"edges":[59],"are":[60,108,350],"size":[62],"<inline-formula":[67,96,129,156,181,208,245,271,310],"content-type=\"math/mathml\">":[68,97,130,157,182,209,246,272,311],"<mml:math":[69,98,131,158,183,210,247,273,312],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[70,99,132,159,184,211,248,274,313],"alttext=\"normal":[71,314],"upper":[72,280,315],"Delta":[73],"x\">":[74],"<mml:semantics>":[75,101,138,163,189,215,254,284,318],"<mml:mrow>":[76,139,190,255,285],"<mml:mi":[77,293,320],"mathvariant=\"normal\">":[78,294,321],"\u0394":[79],"</mml:mi>":[80,296,323],"<mml:mi>x</mml:mi>":[81],"</mml:mrow>":[82,146,148,195,262,264,301],"<mml:annotation":[83,103,149,168,196,220,265,302,326],"encoding=\"application/x-tex\">\\Delta":[84],"x</mml:annotation>":[85],"</mml:semantics>":[86,105,151,170,198,222,267,305,329],"</mml:math>":[87,106,152,171,199,223,268,306,330],"</inline-formula>":[88,107,153,172,200,224,269,307,331],"only.":[89],"For":[90],"example,":[91],"when":[92],"polynomials":[93],"degree":[95],"alttext=\"k\">":[100],"<mml:mi>k</mml:mi>":[102,140,192,256],"encoding=\"application/x-tex\">k</mml:annotation>":[104],"used":[109],"discontinuous":[112],"Galerkin":[113],"(DG)":[114],"method,":[115,238],"and":[116],"exact":[118,204,338],"solution":[119,205,339],"globally":[121],"smooth,":[122],"DG":[124,237],"method":[125],"alttext=\"k":[133,249],"plus":[134,187,250],"1":[135,251],"slash":[136,252],"2\">":[137,253],"<mml:mo>+</mml:mo>":[141,193,257],"<mml:mn>1</mml:mn>":[142,194,258],"<mml:mrow":[143,259],"class=\"MJX-TeXAtom-ORD\">":[144,260],"<mml:mo>/</mml:mo>":[145,261],"<mml:mn>2</mml:mn>":[147,166,191,218,263,288],"encoding=\"application/x-tex\">k+1/2</mml:annotation>":[150,266],"alttext=\"upper":[160,212,275],"L":[161,213,276],"squared\">":[162,214],"<mml:msup>":[164,216,286],"<mml:mi>L</mml:mi>":[165,217,287],"</mml:msup>":[167,219,289],"encoding=\"application/x-tex\">L^2</mml:annotation>":[169,221],"-norm,":[173],"whereas":[174],"post-processed":[176,240],"approximation":[177,241],"alttext=\"2":[185],"k":[186],"1\">":[188],"encoding=\"application/x-tex\">2k+1</mml:annotation>":[197],";":[201],"only,":[225],"which":[227,336],"no":[229],"convergence":[232],"available":[234],"converges":[242],"squared":[277],"left-parenthesis":[278],"normal":[279],"Omega":[281,316],"0":[282],"right-parenthesis\">":[283],"<mml:mo":[290,299],"stretchy=\"false\">(</mml:mo>":[291],"<mml:msub>":[292,319],"\u03a9":[295,322],"<mml:mn>0</mml:mn>":[297,324],"</mml:msub>":[298,325],"stretchy=\"false\">)</mml:mo>":[300],"encoding=\"application/x-tex\">L^2(\\Omega":[303],"_0)</mml:annotation>":[304],",":[308],"where":[309],"0\">":[317],"encoding=\"application/x-tex\">\\Omega":[327],"_0</mml:annotation>":[328],"subdomain":[334],"over":[335],"smooth.":[341],"Numerical":[342],"results":[343],"displaying":[344],"sharpness":[346],"estimates":[349],"presented.":[351]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":14},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":6}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
