{"id":"https://openalex.org/W3112523565","doi":"https://doi.org/10.1137/20m1316962","title":"A Combined-Mode Fourier Analysis of DG Methods for Linear Parabolic Problems","display_name":"A Combined-Mode Fourier Analysis of DG Methods for Linear Parabolic Problems","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3112523565","doi":"https://doi.org/10.1137/20m1316962","mag":"3112523565"},"language":"en","primary_location":{"id":"doi:10.1137/20m1316962","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1316962","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057508300","display_name":"Mohammad Alhawwary","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mohammad Alhawwary","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-0548-840X","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5115861820","display_name":"Zhijian Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhijian Wang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0804,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.74467573,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"42","issue":"6","first_page":"A3825","last_page":"A3858"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9991999864578247,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9987000226974487,"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/wavenumber","display_name":"Wavenumber","score":0.8200305700302124},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.6522136926651001},{"id":"https://openalex.org/keywords/spurious-relationship","display_name":"Spurious relationship","score":0.6410542130470276},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5519383549690247},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5482068061828613},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5329709053039551},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5122289061546326},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.49913644790649414},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.48048320412635803},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.46685200929641724},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46265774965286255},{"id":"https://openalex.org/keywords/dispersion","display_name":"Dispersion (optics)","score":0.4453945457935333},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.41796013712882996},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.4157971739768982},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37808409333229065},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3695392608642578},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.08665880560874939},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06937286257743835},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.06600064039230347}],"concepts":[{"id":"https://openalex.org/C121130766","wikidata":"https://www.wikidata.org/wiki/Q192510","display_name":"Wavenumber","level":2,"score":0.8200305700302124},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.6522136926651001},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.6410542130470276},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5519383549690247},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5482068061828613},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5329709053039551},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5122289061546326},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.49913644790649414},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.48048320412635803},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.46685200929641724},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46265774965286255},{"id":"https://openalex.org/C177562468","wikidata":"https://www.wikidata.org/wiki/Q182893","display_name":"Dispersion (optics)","level":2,"score":0.4453945457935333},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.41796013712882996},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.4157971739768982},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37808409333229065},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3695392608642578},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.08665880560874939},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06937286257743835},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06600064039230347},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.0},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1316962","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1316962","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.8100000023841858}],"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/G1761104186","display_name":null,"funder_award_id":"W911NF-15-1-0505","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G230078430","display_name":null,"funder_award_id":"FA9550-16","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G3392305090","display_name":null,"funder_award_id":"-16-1-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G3616359867","display_name":null,"funder_award_id":"FA9550-16-1","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5385673730","display_name":null,"funder_award_id":"W911NF-15-1-","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G5809100787","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/G6576243381","display_name":null,"funder_award_id":"FA9550-16-1-0128","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"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":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W755493078","https://openalex.org/W1996858170","https://openalex.org/W2002083525","https://openalex.org/W2005576690","https://openalex.org/W2007617472","https://openalex.org/W2010517168","https://openalex.org/W2012833431","https://openalex.org/W2012938047","https://openalex.org/W2018711986","https://openalex.org/W2039115741","https://openalex.org/W2046734098","https://openalex.org/W2049738452","https://openalex.org/W2062004379","https://openalex.org/W2071408075","https://openalex.org/W2078229874","https://openalex.org/W2079263908","https://openalex.org/W2082890708","https://openalex.org/W2100903519","https://openalex.org/W2108231114","https://openalex.org/W2111943775","https://openalex.org/W2128755307","https://openalex.org/W2129600761","https://openalex.org/W2130350269","https://openalex.org/W2333301126","https://openalex.org/W2334162480","https://openalex.org/W2337077802","https://openalex.org/W2509790526","https://openalex.org/W2560325115","https://openalex.org/W2785951528","https://openalex.org/W2793261261","https://openalex.org/W2799173744","https://openalex.org/W4252060206"],"related_works":["https://openalex.org/W2389517732","https://openalex.org/W3099809193","https://openalex.org/W346881876","https://openalex.org/W2084108921","https://openalex.org/W4388240777","https://openalex.org/W2607759403","https://openalex.org/W2106562951","https://openalex.org/W281041820","https://openalex.org/W4308910509","https://openalex.org/W2625153239"],"abstract_inverted_index":{"Fourier":[0,21],"analysis":[1,22,183],"has":[2],"been":[3],"shown":[4],"to":[5,23,95],"provide":[6,200],"valuable":[7],"insight":[8],"into":[9],"the":[10,45,50,58,71,77,92,107,112,119,133,145,149,204,207,217,225],"dispersion":[11,51],"and":[12,52,64,128,139,160,195,222,224,227],"dissipation":[13,53],"characteristics":[14],"of":[15,42,57,98,126,171,187,206],"numerical":[16],"schemes":[17],"for":[18,48,76,101,106,148,168,191],"PDEs.":[19],"Applying":[20],"discontinuous":[24],"Galerkin":[25],"(DG)":[26],"methods":[27,100,190,215],"results":[28,232],"in":[29,81,142,193],"an":[30],"eigenvalue":[31],"problem":[32],"with":[33,144],"multiple":[34],"eigenmodes.":[35],"It":[36],"was":[37,61,74],"often":[38],"relied":[39],"on":[40,203,210],"one":[41,194],"these":[43],"modes,":[44],"so-called":[46],"physical-mode,":[47],"studying":[49],"behavior.":[54,212],"The":[55,213,231],"effect":[56],"other":[59],"modes":[60,84],"considered":[62,214],"spurious":[63],"typically":[65],"neglected.":[66],"Recently,":[67],"a":[68,96,123,180,185,201],"new":[69],"approach,":[70,73],"combined-mode":[72,93,134],"proposed":[75],"linear":[78,108],"wave":[79],"equation,":[80,111],"which":[82],"all":[83],"are":[85,165,233],"considered.":[86],"In":[87,131],"this":[88,176],"paper,":[89],"we":[90,178],"apply":[91],"approach":[94,154,177],"number":[97,186],"DG":[99,189,229],"diffusion.":[102],"We":[103,198],"show":[104],"that":[105,157],"parabolic":[109],"heat":[110],"physical-mode":[113],"behavior":[114,135],"is":[115,136],"completely":[116],"different":[117,167],"than":[118],"exact":[120,146],"diffusion,":[121],"over":[122],"wide":[124],"range":[125],"wavenumbers,":[127],"sometimes":[129],"nondissipative.":[130],"contrast,":[132],"more":[137],"consistent":[138],"sufficiently":[140],"accurate":[141],"comparison":[143],"diffusion":[147,163,182,192],"whole":[150],"wavenumber":[151],"range.":[152],"This":[153],"also":[155,199],"revealed":[156],"short":[158],"time":[159,162],"long":[161],"behaviors":[164],"very":[166],"high-order":[169],"multi--degrees":[170],"freedom":[172],"methods.":[173,230],"Additionally,":[174],"using":[175],"conduct":[179],"comparative":[181],"between":[184],"popular":[188],"two":[196],"dimensions.":[197],"study":[202],"influence":[205],"penalty":[208],"parameter":[209],"their":[211],"include":[216],"symmetric":[218],"interior":[219],"penalty,":[220],"Bassi":[221],"Rebay,":[223],"local":[226],"compact":[228],"verified":[234],"numerically":[235],"through":[236],"several":[237],"test":[238],"cases.":[239]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2020-12-21T00:00:00"}