{"id":"https://openalex.org/W3178702969","doi":"https://doi.org/10.1137/21m1432922","title":"A Conservative and Energy Stable Discontinuous Spectral Element Method for the Shifted Wave Equation in Second Order Form","display_name":"A Conservative and Energy Stable Discontinuous Spectral Element Method for the Shifted Wave Equation in Second Order Form","publication_year":2022,"publication_date":"2022-07-05","ids":{"openalex":"https://openalex.org/W3178702969","doi":"https://doi.org/10.1137/21m1432922","mag":"3178702969"},"language":"en","primary_location":{"id":"doi:10.1137/21m1432922","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1432922","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/A5057355656","display_name":"Kenneth Duru","orcid":"https://orcid.org/0000-0002-5260-7942"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]},{"id":"https://openalex.org/I2802631561","display_name":"Australian Mathematical Sciences Institute","ror":"https://ror.org/00yn60108","country_code":"AU","type":"other","lineage":["https://openalex.org/I2802631561"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Kenneth Duru","raw_affiliation_strings":["Corresponding author. Mathematical Sciences Institute, The Australian National University, Canberra, Aus-tralia"],"raw_orcid":"https://orcid.org/0000-0002-5260-7942","affiliations":[{"raw_affiliation_string":"Corresponding author. Mathematical Sciences Institute, The Australian National University, Canberra, Aus-tralia","institution_ids":["https://openalex.org/I118347636","https://openalex.org/I2802631561"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100772858","display_name":"Siyang Wang","orcid":"https://orcid.org/0000-0002-7954-1576"},"institutions":[{"id":"https://openalex.org/I90267481","display_name":"Ume\u00e5 University","ror":"https://ror.org/05kb8h459","country_code":"SE","type":"education","lineage":["https://openalex.org/I90267481"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Siyang Wang","raw_affiliation_strings":["Department of Mathematics and Mathematical Statistics, Ume\u00e5 University, Ume\u00e5, Sweden"],"raw_orcid":"https://orcid.org/0000-0002-7954-1576","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Mathematical Statistics, Ume\u00e5 University, Ume\u00e5, Sweden","institution_ids":["https://openalex.org/I90267481"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040983203","display_name":"Kenny Wiratama","orcid":"https://orcid.org/0000-0003-0475-9180"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]},{"id":"https://openalex.org/I2802631561","display_name":"Australian Mathematical Sciences Institute","ror":"https://ror.org/00yn60108","country_code":"AU","type":"other","lineage":["https://openalex.org/I2802631561"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Kenny Wiratama","raw_affiliation_strings":["Mathematical Sciences Institute, The Australian National University, Canberra, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Sciences Institute, The Australian National University, Canberra, Australia","institution_ids":["https://openalex.org/I2802631561","https://openalex.org/I118347636"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5057355656"],"corresponding_institution_ids":["https://openalex.org/I118347636","https://openalex.org/I2802631561"],"apc_list":null,"apc_paid":null,"fwci":0.3323,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.47310621,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"60","issue":"4","first_page":"1631","last_page":"1664"},"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":0.9986000061035156,"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":0.9986000061035156,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9959999918937683,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8133224248886108},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.6942941546440125},{"id":"https://openalex.org/keywords/quadrilateral","display_name":"Quadrilateral","score":0.633364200592041},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5840712189674377},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5790819525718689},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.5616710782051086},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5198298096656799},{"id":"https://openalex.org/keywords/hexahedron","display_name":"Hexahedron","score":0.5051103234291077},{"id":"https://openalex.org/keywords/spectral-element-method","display_name":"Spectral element method","score":0.4854739010334015},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.4853936433792114},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4629126191139221},{"id":"https://openalex.org/keywords/conservation-of-energy","display_name":"Conservation of energy","score":0.44672664999961853},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.42629989981651306},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38547542691230774},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.2837579548358917},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09723255038261414}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8133224248886108},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.6942941546440125},{"id":"https://openalex.org/C151756577","wikidata":"https://www.wikidata.org/wiki/Q36810","display_name":"Quadrilateral","level":3,"score":0.633364200592041},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5840712189674377},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5790819525718689},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.5616710782051086},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5198298096656799},{"id":"https://openalex.org/C22411076","wikidata":"https://www.wikidata.org/wiki/Q668113","display_name":"Hexahedron","level":3,"score":0.5051103234291077},{"id":"https://openalex.org/C38961997","wikidata":"https://www.wikidata.org/wiki/Q7575186","display_name":"Spectral element method","level":4,"score":0.4854739010334015},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.4853936433792114},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4629126191139221},{"id":"https://openalex.org/C52957995","wikidata":"https://www.wikidata.org/wiki/Q11382","display_name":"Conservation of energy","level":2,"score":0.44672664999961853},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.42629989981651306},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38547542691230774},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.2837579548358917},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09723255038261414},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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":1,"locations":[{"id":"doi:10.1137/21m1432922","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1432922","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":[],"funders":[{"id":"https://openalex.org/F4320320431","display_name":"Australian National University","ror":"https://ror.org/019wvm592"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W1965804527","https://openalex.org/W1970263005","https://openalex.org/W1975036160","https://openalex.org/W1977991023","https://openalex.org/W2002083525","https://openalex.org/W2010818891","https://openalex.org/W2020168202","https://openalex.org/W2023908293","https://openalex.org/W2031567600","https://openalex.org/W2041371741","https://openalex.org/W2049467895","https://openalex.org/W2049991352","https://openalex.org/W2051465806","https://openalex.org/W2051697741","https://openalex.org/W2065766776","https://openalex.org/W2073738371","https://openalex.org/W2089854137","https://openalex.org/W2091472088","https://openalex.org/W2092855091","https://openalex.org/W2102080986","https://openalex.org/W2104853465","https://openalex.org/W2108334595","https://openalex.org/W2109448994","https://openalex.org/W2112256196","https://openalex.org/W2113972433","https://openalex.org/W2120920736","https://openalex.org/W2126092018","https://openalex.org/W2146272509","https://openalex.org/W2155432414","https://openalex.org/W2179614604","https://openalex.org/W2209133793","https://openalex.org/W2317341383","https://openalex.org/W2338016003","https://openalex.org/W2921034323","https://openalex.org/W2982558606","https://openalex.org/W2987774299","https://openalex.org/W2996135568","https://openalex.org/W3099977586","https://openalex.org/W3158815703","https://openalex.org/W4247375400"],"related_works":["https://openalex.org/W1968086293","https://openalex.org/W2119558010","https://openalex.org/W2062207398","https://openalex.org/W2056063496","https://openalex.org/W246128123","https://openalex.org/W2023838565","https://openalex.org/W2073387455","https://openalex.org/W1513480254","https://openalex.org/W3034882149","https://openalex.org/W2047352485"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"develop":[4],"a":[5],"provably":[6],"energy":[7,55,68],"stable":[8],"and":[9,30,48,57,62,86,99,106,112,123],"conservative":[10],"discontinuous":[11,50],"spectral":[12,46],"element":[13],"method":[14,26],"for":[15,70],"the":[16,28,34,40,45,49,58,67,71,87,109],"shifted":[17,73],"wave":[18,74],"equation":[19,75],"in":[20,66,76,104],"second":[21,77],"order":[22,78],"form.":[23,79],"The":[24,80],"proposed":[25],"combines":[27],"advantages":[29],"central":[31],"ideas":[32],"of":[33,97,116],"following":[35],"very":[36],"successful":[37],"numerical":[38,118],"techniques:":[39],"summation-by-parts":[41],"finite":[42],"difference":[43],"method,":[44,47],"Galerkin":[51],"method.":[52],"We":[53],"prove":[54],"stability":[56],"discrete":[59,83],"conservation":[60,84],"principle":[61],"derive":[63],"error":[64,88],"estimates":[65,89],"norm":[69],"(1+1)-dimensions":[72,105],"energy-stability":[81],"results,":[82],"principle,":[85],"generalize":[90],"to":[91],"multiple":[92],"dimensions":[93],"using":[94],"tensor":[95],"products":[96],"quadrilateral":[98],"hexahedral":[100],"elements.":[101],"Numerical":[102],"experiments,":[103],"(2+1)-dimensions,":[107],"verify":[108],"theoretical":[110],"results":[111],"demonstrate":[113],"optimal":[114],"convergence":[115],"$L^2$":[117],"errors":[119],"at":[120],"subsonic,":[121],"sonic":[122],"supersonic":[124],"regimes.":[125]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}