{"id":"https://openalex.org/W2317341383","doi":"https://doi.org/10.1090/mcom/3090","title":"\ud835\udc3f\u00b2 stable discontinuous Galerkin methods for one-dimensional two-way wave equations","display_name":"\ud835\udc3f\u00b2 stable discontinuous Galerkin methods for one-dimensional two-way wave equations","publication_year":2015,"publication_date":"2015-08-06","ids":{"openalex":"https://openalex.org/W2317341383","doi":"https://doi.org/10.1090/mcom/3090","mag":"2317341383"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3090","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3090","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","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/A5002089116","display_name":"Yingda Cheng","orcid":"https://orcid.org/0000-0003-3229-2979"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yingda Cheng","raw_affiliation_strings":["Department of Mathematics, Michigan State University, East Lansing, Michigan 48824"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Michigan State University, East Lansing, Michigan 48824","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056610892","display_name":"Ching\u2010Shan Chou","orcid":"https://orcid.org/0000-0001-8954-4845"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ching-Shan Chou","raw_affiliation_strings":["Department of Mathematics, The Ohio State University, Columbus, Ohio 43210"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Ohio State University, Columbus, Ohio 43210","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101926587","display_name":"Fengyan Li","orcid":"https://orcid.org/0000-0002-2386-7702"},"institutions":[{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fengyan Li","raw_affiliation_strings":["Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180","institution_ids":["https://openalex.org/I165799507"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021293562","display_name":"Yulong Xing","orcid":"https://orcid.org/0000-0002-3504-6194"},"institutions":[{"id":"https://openalex.org/I103635307","display_name":"University of California, Riverside","ror":"https://ror.org/03nawhv43","country_code":"US","type":"education","lineage":["https://openalex.org/I103635307"]},{"id":"https://openalex.org/I1289243028","display_name":"Oak Ridge National Laboratory","ror":"https://ror.org/01qz5mb56","country_code":"US","type":"facility","lineage":["https://openalex.org/I1289243028","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I4210159294"]},{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yulong Xing","raw_affiliation_strings":["Computer Science and Mathematics Division, Oak Ridge Nationalist Laboratory, Oak Ridge, Tennessee 37831 \u00e2\u0080\u0093 and \u00e2\u0080\u0093 Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996","Department of Mathematics, University of California Riverside, Riverside, California 92521","Computer Science and Mathematics Division, Oak Ridge Nationalist Laboratory, Oak Ridge, Tennessee 37831 \u2013 and \u2013 Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science and Mathematics Division, Oak Ridge Nationalist Laboratory, Oak Ridge, Tennessee 37831 \u00e2\u0080\u0093 and \u00e2\u0080\u0093 Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996","institution_ids":["https://openalex.org/I1289243028","https://openalex.org/I75027704"]},{"raw_affiliation_string":"Department of Mathematics, University of California Riverside, Riverside, California 92521","institution_ids":["https://openalex.org/I103635307"]},{"raw_affiliation_string":"Computer Science and Mathematics Division, Oak Ridge Nationalist Laboratory, Oak Ridge, Tennessee 37831 \u2013 and \u2013 Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996","institution_ids":["https://openalex.org/I1289243028","https://openalex.org/I75027704"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.4392,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.9288871,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"86","issue":"303","first_page":"121","last_page":"155"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994000196456909,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9993000030517578,"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":0.9988999962806702,"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/mathematics","display_name":"Mathematics","score":0.7944246530532837},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7408278584480286},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.5754523873329163},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5657882690429688},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.539788544178009},{"id":"https://openalex.org/keywords/superconvergence","display_name":"Superconvergence","score":0.5279813408851624},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5052641034126282},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4346126914024353},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.433519572019577},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.422148197889328},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.33517828583717346},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13744908571243286},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09043765068054199}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7944246530532837},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7408278584480286},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.5754523873329163},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5657882690429688},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.539788544178009},{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.5279813408851624},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5052641034126282},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4346126914024353},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.433519572019577},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.422148197889328},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.33517828583717346},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13744908571243286},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09043765068054199},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/3090","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3090","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.46000000834465027,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G2902265036","display_name":null,"funder_award_id":"DMS-0847241","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3882871581","display_name":"Development of high-order accurate numerical methods for the shallow-water equations and other hyperbolic conversation laws with source terms","funder_award_id":"1216454","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6183929811","display_name":null,"funder_award_id":"DMS-1318409","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":42,"referenced_works":["https://openalex.org/W12295418","https://openalex.org/W49087508","https://openalex.org/W118329571","https://openalex.org/W1507767947","https://openalex.org/W1555627060","https://openalex.org/W1624046616","https://openalex.org/W1791091458","https://openalex.org/W1912930600","https://openalex.org/W1973481688","https://openalex.org/W1975036160","https://openalex.org/W1982465309","https://openalex.org/W1986784896","https://openalex.org/W1993923624","https://openalex.org/W2002083525","https://openalex.org/W2012833431","https://openalex.org/W2021532548","https://openalex.org/W2041523977","https://openalex.org/W2049351608","https://openalex.org/W2049467895","https://openalex.org/W2052372846","https://openalex.org/W2059659059","https://openalex.org/W2064266313","https://openalex.org/W2070281201","https://openalex.org/W2083855576","https://openalex.org/W2087705056","https://openalex.org/W2097520505","https://openalex.org/W2108334595","https://openalex.org/W2112082878","https://openalex.org/W2114019248","https://openalex.org/W2116729868","https://openalex.org/W2118341834","https://openalex.org/W2129600761","https://openalex.org/W2142063750","https://openalex.org/W2148330860","https://openalex.org/W2159094357","https://openalex.org/W2167377577","https://openalex.org/W2230806989","https://openalex.org/W2319419200","https://openalex.org/W2479395228","https://openalex.org/W2950223431","https://openalex.org/W3010292040","https://openalex.org/W4252060206"],"related_works":["https://openalex.org/W2019032602","https://openalex.org/W4318305492","https://openalex.org/W4389778560","https://openalex.org/W3199641408","https://openalex.org/W2597229022","https://openalex.org/W2947552135","https://openalex.org/W2014920306","https://openalex.org/W2984453791","https://openalex.org/W1982175859","https://openalex.org/W3140967440"],"abstract_inverted_index":{"Simulating":[0],"wave":[1,19],"propagation":[2],"is":[3,117],"one":[4],"of":[5,25,54,114,122,229,245,265],"the":[6,123,204,218,226,230,233,237,243,249,259,262,266],"fundamental":[7],"problems":[8],"in":[9],"scientific":[10],"computing.":[11],"In":[12],"this":[13,115,211],"paper,":[14],"we":[15,78],"consider":[16],"one-dimensional":[17],"two-way":[18],"equations,":[20],"and":[21,106,109,199,206,220,236,241,261],"investigate":[22],"a":[23,51,120],"family":[24],"<inline-formula":[26,59,89,127,153,180],"content-type=\"math/mathml\">":[27,60,90,128,154,181],"<mml:math":[28,61,91,129,155,182],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[29,62,92,130,156,183],"alttext=\"upper":[30,63,93,184],"L":[31,64,94,185],"squared\">":[32,65,95,186],"<mml:semantics>":[33,66,96,133,159,187],"<mml:msup>":[34,67,97,188],"<mml:mi>L</mml:mi>":[35,68,98,189],"<mml:mn>2</mml:mn>":[36,69,99,190],"</mml:msup>":[37,70,100,191],"<mml:annotation":[38,71,101,142,168,192],"encoding=\"application/x-tex\">L^2</mml:annotation>":[39,72,102,193],"</mml:semantics>":[40,73,103,145,171,194],"</mml:math>":[41,74,104,146,172,195],"</inline-formula>":[42,75,105,147,173,196],"stable":[43,76],"high":[44],"order":[45],"discontinuous":[46],"Galerkin":[47,150],"methods":[48,151,231,267],"defined":[49],"through":[50],"general":[52],"form":[53],"numerical":[55,124,246],"fluxes.":[56],"For":[57],"these":[58],"methods,":[77],"systematically":[79],"establish":[80],"stability":[81],"(hence":[82],"energy":[83],"conservation),":[84],"error":[85,197],"estimates":[86,198],"(in":[87],"both":[88,203,217],"negative-order":[107],"norms),":[108],"dispersion":[110],"analysis.":[111],"One":[112],"novelty":[113],"work":[116],"to":[118,177,210,257],"identify":[119],"sub-family":[121],"fluxes,":[125],"termed":[126],"alttext=\"alpha":[131,157],"beta\">":[132,158],"<mml:mrow>":[134,160],"<mml:mi>":[135,138,161,164],"\u03b1":[136,162],"</mml:mi>":[137,140,163,166],"\u03b2":[139,165],"</mml:mrow>":[141,167],"encoding=\"application/x-tex\">\\alpha":[143,169],"\\beta</mml:annotation>":[144,170],"-fluxes.":[148],"Discontinuous":[149],"with":[152],"-fluxes":[174],"are":[175,255],"proven":[176],"have":[178],"optimal":[179],"superconvergence":[200],"properties.":[201],"Moreover,":[202],"upwind":[205],"alternating":[207],"fluxes":[208],"belong":[209],"sub-family.":[212],"Dispersion":[213],"analysis,":[214],"which":[215],"examines":[216],"physical":[219],"spurious":[221],"modes,":[222],"provides":[223],"insights":[224],"into":[225],"sub-optimal":[227],"accuracy":[228,260],"using":[232],"central":[234],"flux":[235],"odd":[238],"degree":[239],"polynomials,":[240],"demonstrates":[242],"importance":[244],"initialization":[247],"for":[248],"proposed":[250],"non-dissipative":[251],"schemes.":[252],"Numerical":[253],"examples":[254],"presented":[256],"illustrate":[258],"long-term":[263],"behavior":[264],"under":[268],"consideration.":[269]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
