{"id":"https://openalex.org/W1978440253","doi":"https://doi.org/10.1137/060661612","title":"Norm Preconditioners for Discontinuous Galerkin $hp$-Finite Element Methods","display_name":"Norm Preconditioners for Discontinuous Galerkin $hp$-Finite Element Methods","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1978440253","doi":"https://doi.org/10.1137/060661612","mag":"1978440253"},"language":"en","primary_location":{"id":"doi:10.1137/060661612","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060661612","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://figshare.com/articles/report/Norm_Preconditioners_for_discontinuous_Galerkin_hp-Finite_Element_methods_/10083284","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103928074","display_name":"Emmanuil H. Georgoulis","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Emmanuil H. Georgoulis","raw_affiliation_strings":["Emmanuil.Georgoulis@mcs.le.ac.uk#TAB#"],"affiliations":[{"raw_affiliation_string":"Emmanuil.Georgoulis@mcs.le.ac.uk#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111847460","display_name":"Daniel Loghin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Loghin","raw_affiliation_strings":["d.loghin@bham.ac.uk#TAB#"],"affiliations":[{"raw_affiliation_string":"d.loghin@bham.ac.uk#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103928074"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3816,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.63422283,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"30","issue":"5","first_page":"2447","last_page":"2465"},"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":0.9997000098228455,"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":0.9997000098228455,"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/T10514","display_name":"Numerical methods in engineering","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9939000010490417,"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/mathematics","display_name":"Mathematics","score":0.8925724029541016},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7370172739028931},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.7044302225112915},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.6913744211196899},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6408705115318298},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6292532682418823},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5961507558822632},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5557352304458618},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5176461338996887},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.4921407103538513},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.47729671001434326},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45425888895988464},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.25527364015579224},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1975492238998413}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8925724029541016},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7370172739028931},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.7044302225112915},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.6913744211196899},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6408705115318298},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6292532682418823},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5961507558822632},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5557352304458618},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5176461338996887},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.4921407103538513},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.47729671001434326},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45425888895988464},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.25527364015579224},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1975492238998413},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/060661612","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060661612","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:figshare.com:article/10083284","is_oa":true,"landing_page_url":"https://figshare.com/articles/report/Norm_Preconditioners_for_discontinuous_Galerkin_hp-Finite_Element_methods_/10083284","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:lra.le.ac.uk:2381/4270","is_oa":false,"landing_page_url":"http://hdl.handle.net/2381/4270","pdf_url":null,"source":{"id":"https://openalex.org/S4306402365","display_name":"Leicester Research Archive (University of Leicester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I153648349","host_organization_name":"University of Leicester","host_organization_lineage":["https://openalex.org/I153648349"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Report"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/d4763737-51e5-402b-a20d-e20613b80fda","is_oa":false,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/d4763737-51e5-402b-a20d-e20613b80fda","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Georgoulis, EH & Loghin, D 2008, 'Norm Preconditioners for Discontinuous Galerkin $hp$-Finite Element Methods', SIAM Journal on Scientific Computing, vol. 30, no. 5, pp. 2447-2465. https://doi.org/10.1137/060661612","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/10083284","is_oa":true,"landing_page_url":"https://figshare.com/articles/report/Norm_Preconditioners_for_discontinuous_Galerkin_hp-Finite_Element_methods_/10083284","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W222841820","https://openalex.org/W639693100","https://openalex.org/W1506342804","https://openalex.org/W1550543785","https://openalex.org/W1947782577","https://openalex.org/W1964968800","https://openalex.org/W1973312823","https://openalex.org/W1973709085","https://openalex.org/W1979771104","https://openalex.org/W1982093974","https://openalex.org/W1982893859","https://openalex.org/W1990319748","https://openalex.org/W1990462076","https://openalex.org/W1992066344","https://openalex.org/W2001837653","https://openalex.org/W2001911203","https://openalex.org/W2008509897","https://openalex.org/W2010517168","https://openalex.org/W2029119302","https://openalex.org/W2029725158","https://openalex.org/W2040011362","https://openalex.org/W2049644675","https://openalex.org/W2062839853","https://openalex.org/W2066637873","https://openalex.org/W2068395392","https://openalex.org/W2070299075","https://openalex.org/W2073753111","https://openalex.org/W2082741499","https://openalex.org/W2093664623","https://openalex.org/W2117221287","https://openalex.org/W2125822172","https://openalex.org/W2137747286","https://openalex.org/W2140153041","https://openalex.org/W2147705138","https://openalex.org/W2156047592","https://openalex.org/W2185249804","https://openalex.org/W2275084433","https://openalex.org/W2415509676","https://openalex.org/W4242960114"],"related_works":["https://openalex.org/W2358905935","https://openalex.org/W3046241855","https://openalex.org/W2139875628","https://openalex.org/W1995427418","https://openalex.org/W70795231","https://openalex.org/W2128313919","https://openalex.org/W2120874885","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2040975642"],"abstract_inverted_index":{"We":[0,34],"consider":[1],"a":[2,21,29],"norm-preconditioning":[3],"approach":[4],"for":[5,37,52],"the":[6,42,53],"solution":[7,26],"of":[8,14,44,49],"discontinuous":[9],"Galerkin":[10],"finite":[11],"element":[12],"discretizations":[13],"second":[15],"order":[16],"partial":[17],"differential":[18],"equations":[19],"with":[20],"nonnegative":[22],"characteristic":[23],"form.":[24],"Our":[25],"method":[27],"is":[28,47],"norm-preconditioned":[30],"three-term":[31],"GMRES":[32],"routine.":[33],"find":[35],"that":[36],"symmetric":[38],"positive-definite":[39],"diffusivity":[40],"tensors":[41],"convergence":[43],"our":[45],"solver":[46],"independent":[48],"discretization,":[50],"while":[51],"semidefinite":[54],"case":[55],"both":[56,63],"theory":[57],"and":[58,65],"experiment":[59],"indicate":[60],"dependence":[61],"on":[62,74],"h":[64],"p.":[66],"Numerical":[67],"results":[68],"are":[69],"included":[70],"to":[71],"illustrate":[72],"performance":[73],"several":[75],"test":[76],"cases.":[77]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
