{"id":"https://openalex.org/W1993443533","doi":"https://doi.org/10.1090/s0025-5718-10-02334-3","title":"A projection-based error analysis of HDG methods","display_name":"A projection-based error analysis of HDG methods","publication_year":2010,"publication_date":"2010-03-18","ids":{"openalex":"https://openalex.org/W1993443533","doi":"https://doi.org/10.1090/s0025-5718-10-02334-3","mag":"1993443533"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-10-02334-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-10-02334-3","pdf_url":"https://www.ams.org/mcom/2010-79-271/S0025-5718-10-02334-3/S0025-5718-10-02334-3.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":"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":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2010-79-271/S0025-5718-10-02334-3/S0025-5718-10-02334-3.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, Vincent Hall, Minneapolis, Minnesota 55455"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Minnesota, Vincent Hall, Minneapolis, Minnesota 55455","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022236310","display_name":"Jay Gopalakrishnan","orcid":"https://orcid.org/0000-0001-7508-3232"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jayadeep Gopalakrishnan","raw_affiliation_strings":["Department of Mathematics, University of Florida, Gainesville, Florida 32611\u00e2\u0080\u00938105","Department of Mathematics University of Florida Gainesville, Florida 32611-8105"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Florida, Gainesville, Florida 32611\u00e2\u0080\u00938105","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"Department of Mathematics University of Florida Gainesville, Florida 32611-8105","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109302308","display_name":"Francisco-Javier Sayas","orcid":null},"institutions":[{"id":"https://openalex.org/I255234318","display_name":"Universidad de Zaragoza","ror":"https://ror.org/012a91z28","country_code":"ES","type":"education","lineage":["https://openalex.org/I255234318"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Francisco-Javier Sayas","raw_affiliation_strings":["Departamento de Matem\u00c3\u00a1tica Aplicada, CPS, Universidad de Zaragoza, 50018 Zaragoza, Spain","Departamento de Matem\u00e1tica Aplicada, CPS, Universidad de Zaragoza, 50018 Zaragoza, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00c3\u00a1tica Aplicada, CPS, Universidad de Zaragoza, 50018 Zaragoza, Spain","institution_ids":["https://openalex.org/I255234318"]},{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, CPS, Universidad de Zaragoza, 50018 Zaragoza, Spain","institution_ids":["https://openalex.org/I255234318"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":16.0839,"has_fulltext":true,"cited_by_count":301,"citation_normalized_percentile":{"value":0.99487792,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"79","issue":"271","first_page":"1351","last_page":"1367"},"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":1.0,"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":1.0,"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":0.9993000030517578,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.807144045829773},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.806848406791687},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8058195114135742},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6346943378448486},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.606469988822937},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.5796118974685669},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5562910437583923},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5341341495513916},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5223904252052307},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.4443262219429016},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3265289068222046},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3166595697402954},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2891160249710083},{"id":"https://openalex.org/keywords/dykstras-projection-algorithm","display_name":"Dykstra's projection algorithm","score":0.26002925634384155},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.17685282230377197}],"concepts":[{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.807144045829773},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.806848406791687},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8058195114135742},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6346943378448486},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.606469988822937},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.5796118974685669},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5562910437583923},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5341341495513916},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5223904252052307},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.4443262219429016},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3265289068222046},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3166595697402954},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2891160249710083},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.26002925634384155},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.17685282230377197},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1090/s0025-5718-10-02334-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-10-02334-3","pdf_url":"https://www.ams.org/mcom/2010-79-271/S0025-5718-10-02334-3/S0025-5718-10-02334-3.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":"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"},{"id":"pmh:oai:pdxscholar.library.pdx.edu:mth_fac-1053","is_oa":false,"landing_page_url":"https://pdxscholar.library.pdx.edu/mth_fac/54","pdf_url":null,"source":{"id":"https://openalex.org/S4377196300","display_name":"PDXScholar  (Portland State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126345244","host_organization_name":"Portland State University","host_organization_lineage":["https://openalex.org/I126345244"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics and Statistics Faculty Publications and Presentations","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.184.2821","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.184.2821","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.ufl.edu/%7Ejayg/pub/projHDG.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.188.7952","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.188.7952","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/2010-79-271/S0025-5718-10-02334-3/S0025-5718-10-02334-3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.206.167","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.206.167","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/0000-000-00/S0025-5718-10-02334-3/S0025-5718-10-02334-3.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-10-02334-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-10-02334-3","pdf_url":"https://www.ams.org/mcom/2010-79-271/S0025-5718-10-02334-3/S0025-5718-10-02334-3.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":"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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6594343154","display_name":"SCREMS: Developing Computational Mathematics at the University of Florida","funder_award_id":"0619080","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/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"},{"id":"https://openalex.org/F4320309636","display_name":"University of Minnesota","ror":"https://ror.org/03grvy078"},{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320326208","display_name":"Gobierno de Arag\u00f3n","ror":"https://ror.org/0425pg203"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1993443533.pdf","grobid_xml":"https://content.openalex.org/works/W1993443533.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W136185420","https://openalex.org/W1586623601","https://openalex.org/W1975782244","https://openalex.org/W1978682560","https://openalex.org/W1998894128","https://openalex.org/W2008325195","https://openalex.org/W2014339952","https://openalex.org/W2015795390","https://openalex.org/W2033559968","https://openalex.org/W2041523977","https://openalex.org/W2051045979","https://openalex.org/W2051682834","https://openalex.org/W2069036386","https://openalex.org/W2073774784","https://openalex.org/W2078367662","https://openalex.org/W2130350269","https://openalex.org/W2284562107","https://openalex.org/W2299422535","https://openalex.org/W2491027544","https://openalex.org/W2600341198","https://openalex.org/W6812042197","https://openalex.org/W6813285973"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2055696851","https://openalex.org/W2324487000","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2040975642","https://openalex.org/W2107130595","https://openalex.org/W2381742561","https://openalex.org/W1993443533","https://openalex.org/W2004168836"],"abstract_inverted_index":{"We":[0,92],"introduce":[1],"a":[2,22,97,103],"new":[3,23],"technique":[4,16,95],"for":[5],"the":[6,19,30,33,37,41,44,47,59,66,69,79,90,94],"error":[7],"analysis":[8,42],"of":[9,21,32,36,43,46,58,65,76,78,87],"hybridizable":[10],"discontinuous":[11],"Galerkin":[12],"(HDG)":[13],"methods.":[14,38],"The":[15],"relies":[17],"on":[18,96],"use":[20],"projection":[24],"whose":[25],"design":[26],"is":[27],"inspired":[28],"by":[29,89],"form":[31],"numerical":[34],"traces":[35],"This":[39],"renders":[40],"projections":[45,57],"discretization":[48],"errors":[49,60],"simple":[50],"and":[51,71],"concise.":[52],"By":[53],"showing":[54],"that":[55],"these":[56],"are":[61,82],"bounded":[62],"in":[63],"terms":[64],"distance":[67],"between":[68],"solution":[70],"its":[72],"projection,":[73],"our":[74],"studies":[75],"influence":[77],"stabilization":[80],"parameter":[81],"reduced":[83],"to":[84,102],"local":[85],"analyses":[86],"approximation":[88],"projection.":[91],"illustrate":[93],"specific":[98],"HDG":[99],"method":[100],"applied":[101],"model":[104],"second-order":[105],"elliptic":[106],"problem.":[107]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":20},{"year":2024,"cited_by_count":17},{"year":2023,"cited_by_count":18},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":18},{"year":2020,"cited_by_count":25},{"year":2019,"cited_by_count":26},{"year":2018,"cited_by_count":26},{"year":2017,"cited_by_count":23},{"year":2016,"cited_by_count":26},{"year":2015,"cited_by_count":23},{"year":2014,"cited_by_count":19},{"year":2013,"cited_by_count":18},{"year":2012,"cited_by_count":15}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}