{"id":"https://openalex.org/W3022416922","doi":"https://doi.org/10.1137/19m1290966","title":"A Unified Error Analysis of Hybridizable Discontinuous Galerkin Methods for the Static Maxwell Equations","display_name":"A Unified Error Analysis of Hybridizable Discontinuous Galerkin Methods for the Static Maxwell Equations","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3022416922","doi":"https://doi.org/10.1137/19m1290966","mag":"3022416922"},"language":"en","primary_location":{"id":"doi:10.1137/19m1290966","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1290966","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041013363","display_name":"Shukai Du","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Shukai Du","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5017262284","display_name":"Francisco\u2010Javier Sayas","orcid":"https://orcid.org/0000-0003-0321-2183"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Francisco-Javier Sayas","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5041013363"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2888,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.87231128,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":98},"biblio":{"volume":"58","issue":"2","first_page":"1367","last_page":"1391"},"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":0.9997000098228455,"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":0.9987999796867371,"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/superconvergence","display_name":"Superconvergence","score":0.8649184107780457},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7768706679344177},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.6863164901733398},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.636867344379425},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.5371596813201904},{"id":"https://openalex.org/keywords/maxwells-equations","display_name":"Maxwell's equations","score":0.5004479885101318},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.49134817719459534},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.474712997674942},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.3597955107688904},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28844714164733887},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09903869032859802}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.8649184107780457},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7768706679344177},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.6863164901733398},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.636867344379425},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.5371596813201904},{"id":"https://openalex.org/C59282198","wikidata":"https://www.wikidata.org/wiki/Q51501","display_name":"Maxwell's equations","level":2,"score":0.5004479885101318},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.49134817719459534},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.474712997674942},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3597955107688904},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28844714164733887},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09903869032859802},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1290966","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1290966","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5368281484","display_name":null,"funder_award_id":"DMS-1818867","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":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1902428307","https://openalex.org/W1935825599","https://openalex.org/W1973990119","https://openalex.org/W1976184877","https://openalex.org/W1993443533","https://openalex.org/W1998894128","https://openalex.org/W2014310302","https://openalex.org/W2035543412","https://openalex.org/W2043140788","https://openalex.org/W2051682834","https://openalex.org/W2062618977","https://openalex.org/W2064909895","https://openalex.org/W2067527388","https://openalex.org/W2073432708","https://openalex.org/W2087592144","https://openalex.org/W2090064304","https://openalex.org/W2090343972","https://openalex.org/W2130350269","https://openalex.org/W2143783905","https://openalex.org/W2148849010","https://openalex.org/W2153685664","https://openalex.org/W2158006240","https://openalex.org/W2160151186","https://openalex.org/W2166587858","https://openalex.org/W2296275512","https://openalex.org/W2333408843","https://openalex.org/W2376378314","https://openalex.org/W2794122374","https://openalex.org/W2964155488","https://openalex.org/W4246353874"],"related_works":["https://openalex.org/W2048180566","https://openalex.org/W1002850520","https://openalex.org/W2594236274","https://openalex.org/W2999429935","https://openalex.org/W3089630606","https://openalex.org/W2477989241","https://openalex.org/W2027195596","https://openalex.org/W2945672503","https://openalex.org/W3022416922","https://openalex.org/W4300232707"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2],"framework":[3],"that":[4,36,84,92],"allows":[5],"us":[6],"to":[7,31,122,137,158],"analyze":[8,48],"different":[9,145],"variants":[10,50,87,93],"of":[11,34,41,51,62,114,144],"hybridizable":[12],"discontinuous":[13],"Galerkin":[14],"(HDG)":[15],"methods":[16,53,139],"for":[17],"the":[18,29,32,39,42,70,102,115,118,123,142,149,152,160],"static":[19],"Maxwell":[20],"equations":[21],"using":[22],"one":[23],"simple":[24],"analysis.":[25,161],"It":[26],"reduces":[27],"all":[28,85],"work":[30],"construction":[33],"projections":[35],"best":[37],"fit":[38],"structures":[40],"approximation":[43],"spaces.":[44],"As":[45],"applications,":[46],"we":[47,82,106,133,154],"four":[49,86],"HDG":[52],"(denoted":[54],"by":[55],"$\\mathfrak{B}$,":[56],"$\\mathfrak{H}$,":[57,67],"$\\mathfrak{B+}$,":[58],"$\\mathfrak{H+}$),":[59],"where":[60],"two":[61,72,103],"them":[63],"are":[64,73,88],"known":[65,104],"(variants":[66,75],"$\\mathfrak{B+}$)":[68],"and":[69,91,95,117,140],"other":[71],"new":[74,124],"$\\mathfrak{H+}$,":[76],"$\\mathfrak{B}$).":[77],"Under":[78],"certain":[79],"regularity":[80],"assumptions,":[81],"show":[83],"optimally":[89],"convergent":[90],"$\\mathfrak{B+}$":[94],"$\\mathfrak{H+}$":[96],"achieve":[97],"superconvergence":[98],"without":[99],"postprocessing.":[100],"For":[101,129],"variants,":[105],"prove":[107],"their":[108],"optimal":[109],"convergence":[110],"under":[111],"weaker":[112],"requirements":[113],"meshes":[116],"stabilization":[119,146],"functions":[120,147],"thanks":[121],"analysis":[125,136],"techniques":[126],"being":[127],"introduced.":[128],"solution":[130],"with":[131],"low-regularity,":[132],"give":[134],"an":[135],"these":[138],"investigate":[141],"effect":[143],"on":[148],"convergence.":[150],"At":[151],"end,":[153],"provide":[155],"numerical":[156],"experiments":[157],"support":[159]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
