{"id":"https://openalex.org/W2949289096","doi":"https://doi.org/10.1090/s0025-5718-2014-02885-8","title":"Spectral approximations by the HDG method","display_name":"Spectral approximations by the HDG method","publication_year":2014,"publication_date":"2014-12-30","ids":{"openalex":"https://openalex.org/W2949289096","doi":"https://doi.org/10.1090/s0025-5718-2014-02885-8","mag":"2949289096"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2014-02885-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2014-02885-8","pdf_url":"https://www.ams.org/mcom/2015-84-293/S0025-5718-2014-02885-8/S0025-5718-2014-02885-8.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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2015-84-293/S0025-5718-2014-02885-8/S0025-5718-2014-02885-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022236310","display_name":"Jay Gopalakrishnan","orcid":"https://orcid.org/0000-0001-7508-3232"},"institutions":[{"id":"https://openalex.org/I126345244","display_name":"Portland State University","ror":"https://ror.org/00yn2fy02","country_code":"US","type":"education","lineage":["https://openalex.org/I126345244"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Gopalakrishnan","raw_affiliation_strings":["Portland State University, P.O. Box 751, Portland, Oregon 97207-0751"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Portland State University, P.O. Box 751, Portland, Oregon 97207-0751","institution_ids":["https://openalex.org/I126345244"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030904539","display_name":"F. Li","orcid":null},"institutions":[{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"F. Li","raw_affiliation_strings":["Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180","institution_ids":["https://openalex.org/I165799507"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067470754","display_name":"Ngoc Cuong Nguyen","orcid":"https://orcid.org/0000-0001-9167-5780"},"institutions":[{"id":"https://openalex.org/I46020346","display_name":"American Institute of Aeronautics and Astronautics","ror":"https://ror.org/00a1rzv11","country_code":"US","type":"other","lineage":["https://openalex.org/I46020346"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"N.-C. Nguyen","raw_affiliation_strings":["Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139","institution_ids":["https://openalex.org/I46020346","https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108356751","display_name":"J. Peraire","orcid":null},"institutions":[{"id":"https://openalex.org/I46020346","display_name":"American Institute of Aeronautics and Astronautics","ror":"https://ror.org/00a1rzv11","country_code":"US","type":"other","lineage":["https://openalex.org/I46020346"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Peraire","raw_affiliation_strings":["Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139","institution_ids":["https://openalex.org/I46020346","https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8502,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.7444954,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"84","issue":"293","first_page":"1037","last_page":"1059"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9986000061035156,"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"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9966999888420105,"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/mathematics","display_name":"Mathematics","score":0.9102362990379333},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.788885235786438},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.698284387588501},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.6339725255966187},{"id":"https://openalex.org/keywords/rayleigh-quotient","display_name":"Rayleigh quotient","score":0.5264504551887512},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.49671512842178345},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4787123203277588},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47221639752388},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45258718729019165},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.41664597392082214},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.19601574540138245}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9102362990379333},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.788885235786438},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.698284387588501},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.6339725255966187},{"id":"https://openalex.org/C2778158742","wikidata":"https://www.wikidata.org/wiki/Q1665115","display_name":"Rayleigh quotient","level":3,"score":0.5264504551887512},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.49671512842178345},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4787123203277588},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47221639752388},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45258718729019165},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.41664597392082214},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.19601574540138245},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-2014-02885-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2014-02885-8","pdf_url":"https://www.ams.org/mcom/2015-84-293/S0025-5718-2014-02885-8/S0025-5718-2014-02885-8.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:arXiv.org:1207.1181","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1207.1181","pdf_url":"https://arxiv.org/pdf/1207.1181","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.747.1942","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.747.1942","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/1207.1181.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2014-02885-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2014-02885-8","pdf_url":"https://www.ams.org/mcom/2015-84-293/S0025-5718-2014-02885-8/S0025-5718-2014-02885-8.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/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G1615984119","display_name":null,"funder_award_id":"DMS-1318916","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2902265036","display_name":null,"funder_award_id":"DMS-0847241","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5098529204","display_name":"Novel mixed and DG methods","funder_award_id":"1211635","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6071252945","display_name":null,"funder_award_id":"FA9550-12","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6532825974","display_name":null,"funder_award_id":"FA9550-12-0357","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6692275610","display_name":"Discontinuous Petrov Galerkin Methods and Applications","funder_award_id":"1318916","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8921537696","display_name":"CAREER: Development and Applications of Discontinuous Galerkin Methods","funder_award_id":"0847241","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/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2949289096.pdf","grobid_xml":"https://content.openalex.org/works/W2949289096.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1575147392","https://openalex.org/W1965386465","https://openalex.org/W1969462995","https://openalex.org/W1970136394","https://openalex.org/W1973419466","https://openalex.org/W1975014971","https://openalex.org/W1990669907","https://openalex.org/W1993443533","https://openalex.org/W1993578085","https://openalex.org/W1998006824","https://openalex.org/W1998894128","https://openalex.org/W2007707831","https://openalex.org/W2012061418","https://openalex.org/W2013434737","https://openalex.org/W2034617673","https://openalex.org/W2046402929","https://openalex.org/W2091491115","https://openalex.org/W2299422535","https://openalex.org/W2587559127","https://openalex.org/W4243893532","https://openalex.org/W4245413304","https://openalex.org/W4253251115"],"related_works":["https://openalex.org/W2014800978","https://openalex.org/W2061421451","https://openalex.org/W1969730698","https://openalex.org/W1552276833","https://openalex.org/W2132583619","https://openalex.org/W1995228206","https://openalex.org/W4243371733","https://openalex.org/W2147129399","https://openalex.org/W2013379693","https://openalex.org/W3106362747"],"abstract_inverted_index":{"We":[0,21,100],"consider":[1],"the":[2,6,15,29,36,45,48,53,58,83,89,96,110,117],"numerical":[3,59,62,111],"approximation":[4],"of":[5,8,47],"spectrum":[7],"a":[9,66,105],"second-order":[10],"elliptic":[11],"eigenvalue":[12],"problem":[13],"by":[14,114],"hybridizable":[16],"discontinuous":[17],"Galerkin":[18],"(HDG)":[19],"method.":[20,99],"show":[22,64],"for":[23,88,95,109],"problems":[24],"with":[25],"smooth":[26],"eigenfunctions":[27,33],"that":[28,65,79],"approximate":[30,52],"eigenvalues":[31,78],"and":[32,39,57,103],"converge":[34,80],"at":[35,82],"rate":[37,84],"$2k+1$":[38],"$k+1$,":[40],"respectively.":[41],"Here":[42],"$k$":[43],"is":[44],"degree":[46],"polynomials":[49],"used":[50],"to":[51,71],"solution,":[54],"its":[55],"flux,":[56],"traces.":[60],"Our":[61],"studies":[63],"Rayleigh":[67],"quotient-like":[68],"formula":[69],"applied":[70],"certain":[72],"locally":[73],"postprocessed":[74],"approximations":[75],"can":[76],"yield":[77],"faster":[81],"$2k":[85],"+":[86],"2$":[87],"HDG":[90],"method":[91],"as":[92,94],"well":[93],"Brezzi-Douglas-Marini":[97],"(BDM)":[98],"also":[101],"derive":[102],"study":[104],"condensed":[106],"nonlinear":[107],"eigenproblem":[108],"traces":[112],"obtained":[113],"eliminating":[115],"all":[116],"other":[118],"variables.":[119]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}