{"id":"https://openalex.org/W2921034323","doi":"https://doi.org/10.1137/19m1242720","title":"An Energy-Based Discontinuous Galerkin Method for the Wave Equation with Advection","display_name":"An Energy-Based Discontinuous Galerkin Method for the Wave Equation with Advection","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2921034323","doi":"https://doi.org/10.1137/19m1242720","mag":"2921034323"},"language":"en","primary_location":{"id":"doi:10.1137/19m1242720","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1242720","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/A5100388713","display_name":"Lu Zhang","orcid":"https://orcid.org/0000-0003-4009-2969"},"institutions":[{"id":"https://openalex.org/I178169726","display_name":"Southern Methodist University","ror":"https://ror.org/042tdr378","country_code":"US","type":"education","lineage":["https://openalex.org/I178169726"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lu Zhang","raw_affiliation_strings":["Dept. of Mathematics, Southern Methodist University, Dallas TX 75275"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Mathematics, Southern Methodist University, Dallas TX 75275","institution_ids":["https://openalex.org/I178169726"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009161299","display_name":"Thomas Hagstrom","orcid":"https://orcid.org/0000-0002-9775-2051"},"institutions":[{"id":"https://openalex.org/I178169726","display_name":"Southern Methodist University","ror":"https://ror.org/042tdr378","country_code":"US","type":"education","lineage":["https://openalex.org/I178169726"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thomas Hagstrom","raw_affiliation_strings":["Dept. of Mathematics, Southern Methodist University, Dallas TX 75275"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Mathematics, Southern Methodist University, Dallas TX 75275","institution_ids":["https://openalex.org/I178169726"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000111293","display_name":"Daniel Appel\u00f6","orcid":"https://orcid.org/0000-0002-0378-4563"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]},{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel Appel\u00f6","raw_affiliation_strings":["Dept. of Applied Mathematics, University of Colorado, Boulder, Boulder CO 80309"],"raw_orcid":"https://orcid.org/0000-0002-0378-4563","affiliations":[{"raw_affiliation_string":"Dept. of Applied Mathematics, University of Colorado, Boulder, Boulder CO 80309","institution_ids":["https://openalex.org/I188538660","https://openalex.org/I4210131439"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5183,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.56794552,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"57","issue":"5","first_page":"2469","last_page":"2492"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9994999766349792,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9994999766349792,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9991000294685364,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9976000189781189,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.8096038103103638},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7803289890289307},{"id":"https://openalex.org/keywords/advection","display_name":"Advection","score":0.7113927006721497},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6084634065628052},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5836142897605896},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5269069075584412},{"id":"https://openalex.org/keywords/upwind-scheme","display_name":"Upwind scheme","score":0.49752166867256165},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4875282943248749},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.47858142852783203},{"id":"https://openalex.org/keywords/kinetic-energy","display_name":"Kinetic energy","score":0.4776933491230011},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.45896127820014954},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.4308392107486725},{"id":"https://openalex.org/keywords/supersonic-speed","display_name":"Supersonic speed","score":0.42792007327079773},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.2914619445800781},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.19040066003799438},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.17369145154953003},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13326728343963623}],"concepts":[{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.8096038103103638},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7803289890289307},{"id":"https://openalex.org/C5072599","wikidata":"https://www.wikidata.org/wiki/Q379788","display_name":"Advection","level":2,"score":0.7113927006721497},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6084634065628052},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5836142897605896},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5269069075584412},{"id":"https://openalex.org/C94025248","wikidata":"https://www.wikidata.org/wiki/Q7899499","display_name":"Upwind scheme","level":3,"score":0.49752166867256165},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4875282943248749},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.47858142852783203},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.4776933491230011},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.45896127820014954},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.4308392107486725},{"id":"https://openalex.org/C205991772","wikidata":"https://www.wikidata.org/wiki/Q221337","display_name":"Supersonic speed","level":2,"score":0.42792007327079773},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2914619445800781},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.19040066003799438},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.17369145154953003},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13326728343963623},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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:10.1137/19m1242720","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1242720","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":[{"score":0.8899999856948853,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G2781362197","display_name":"Robust High-Order Methods for Wave Equations in the Time Domain","funder_award_id":"1418871","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G693263272","display_name":"Numerical Methods for Wave Equations in Time and Frequency Domain","funder_award_id":"1913076","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1583515859","https://openalex.org/W1966359670","https://openalex.org/W2018334166","https://openalex.org/W2039238961","https://openalex.org/W2049467895","https://openalex.org/W2078229874","https://openalex.org/W2087705056","https://openalex.org/W2128755307","https://openalex.org/W2209133793","https://openalex.org/W2247651270","https://openalex.org/W2934526567","https://openalex.org/W2950426004","https://openalex.org/W3099782930","https://openalex.org/W4237196420"],"related_works":["https://openalex.org/W2081375188","https://openalex.org/W4390079155","https://openalex.org/W958550505","https://openalex.org/W1604457177","https://openalex.org/W3036101264","https://openalex.org/W2163151373","https://openalex.org/W1986676657","https://openalex.org/W3028496900","https://openalex.org/W2162026849","https://openalex.org/W2394687667"],"abstract_inverted_index":{"An":[0],"energy-based":[1,65],"discontinuous":[2,66],"Galerkin":[3,67],"method":[4,60],"for":[5,56,69],"the":[6,24,38,53],"advective":[7],"wave":[8,72],"equation":[9],"is":[10,33],"proposed":[11],"and":[12,27,30,43,87],"analyzed.":[13],"Energy-conserving":[14],"or":[15],"energy-dissipating":[16],"methods":[17,68],"follow":[18],"from":[19],"simple,":[20],"mesh-independent":[21],"choices":[22],"of":[23,85],"interelement":[25],"fluxes,":[26],"both":[28],"subsonic":[29],"supersonic":[31],"advection":[32],"allowed.":[34],"Error":[35],"estimates":[36],"in":[37,52],"energy":[39,78],"norm":[40,55],"are":[41],"established,":[42],"numerical":[44],"experiments":[45],"on":[46,64],"structured":[47],"grids":[48],"display":[49],"optimal":[50],"convergence":[51],"$L^2$":[54],"upwind":[57],"fluxes.":[58],"The":[59],"generalizes":[61],"earlier":[62],"work":[63],"second":[70],"order":[71],"equations":[73],"which":[74],"was":[75],"restricted":[76],"to":[77],"forms":[79],"written":[80],"as":[81],"a":[82],"simple":[83],"sum":[84],"kinetic":[86],"potential":[88],"energy.":[89]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}
