{"id":"https://openalex.org/W2030213082","doi":"https://doi.org/10.1137/s0036142997329554","title":"Higher Order Triangular Finite Elements with Mass Lumping for the Wave Equation","display_name":"Higher Order Triangular Finite Elements with Mass Lumping for the Wave Equation","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2030213082","doi":"https://doi.org/10.1137/s0036142997329554","mag":"2030213082"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142997329554","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142997329554","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/A5109549737","display_name":"Gary Cohen","orcid":null},"institutions":[{"id":"https://openalex.org/I4210146116","display_name":"POEMS: Propagation des Ondes : Etude Math\u00e9matique et Simulationan","ror":"https://ror.org/03gvm2667","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I1326498283","https://openalex.org/I201181511","https://openalex.org/I4210095849","https://openalex.org/I4210126360","https://openalex.org/I4210126360","https://openalex.org/I4210145102","https://openalex.org/I4210146116","https://openalex.org/I4405254745","https://openalex.org/I4405260730"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"G. Cohen","raw_affiliation_strings":["Propagation des Ondes : \u00c9tude Math\u00e9matique et Simulation"],"affiliations":[{"raw_affiliation_string":"Propagation des Ondes : \u00c9tude Math\u00e9matique et Simulation","institution_ids":["https://openalex.org/I4210146116"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112637460","display_name":"Patrick Joly","orcid":null},"institutions":[{"id":"https://openalex.org/I4210146116","display_name":"POEMS: Propagation des Ondes : Etude Math\u00e9matique et Simulationan","ror":"https://ror.org/03gvm2667","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I1326498283","https://openalex.org/I201181511","https://openalex.org/I4210095849","https://openalex.org/I4210126360","https://openalex.org/I4210126360","https://openalex.org/I4210145102","https://openalex.org/I4210146116","https://openalex.org/I4405254745","https://openalex.org/I4405260730"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"P. Joly","raw_affiliation_strings":["Propagation des Ondes : \u00c9tude Math\u00e9matique et Simulation"],"affiliations":[{"raw_affiliation_string":"Propagation des Ondes : \u00c9tude Math\u00e9matique et Simulation","institution_ids":["https://openalex.org/I4210146116"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029383512","display_name":"John E. Roberts","orcid":"https://orcid.org/0000-0003-3830-9807"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. E. Roberts","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5016826877","display_name":"Nathalie Tordjman","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"N. Tordjman","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5109549737"],"corresponding_institution_ids":["https://openalex.org/I4210146116"],"apc_list":null,"apc_paid":null,"fwci":5.2778,"has_fulltext":false,"cited_by_count":229,"citation_normalized_percentile":{"value":0.95161365,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"38","issue":"6","first_page":"2047","last_page":"2078"},"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":0.9994999766349792,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","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/T10514","display_name":"Numerical methods in engineering","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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":0.9990000128746033,"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":0.840263843536377},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7857993841171265},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.7612285614013672},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.694966197013855},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.594393789768219},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.5220275521278381},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4922601282596588},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.48670437932014465},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4598909020423889},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43342846632003784},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.41916564106941223},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06842470169067383}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.840263843536377},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7857993841171265},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.7612285614013672},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.694966197013855},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.594393789768219},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.5220275521278381},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4922601282596588},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.48670437932014465},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4598909020423889},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43342846632003784},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.41916564106941223},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06842470169067383},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142997329554","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142997329554","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"},{"id":"pmh:oai:HAL:hal-01010373v1","is_oa":false,"landing_page_url":"https://ensta.hal.science/hal-01010373","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis, 2001, 38 (6), pp.2047-2078. &#x27E8;10.1137/S0036142997329554&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W42576215","https://openalex.org/W155081664","https://openalex.org/W568020624","https://openalex.org/W1491961545","https://openalex.org/W1515623627","https://openalex.org/W1591608973","https://openalex.org/W1621885647","https://openalex.org/W1674659126","https://openalex.org/W1964757393","https://openalex.org/W1969094857","https://openalex.org/W1975030793","https://openalex.org/W1977052086","https://openalex.org/W1981791075","https://openalex.org/W2011828708","https://openalex.org/W2039280894","https://openalex.org/W2041523977","https://openalex.org/W2050348866","https://openalex.org/W2055031800","https://openalex.org/W2075042757","https://openalex.org/W2081474085","https://openalex.org/W2109911863","https://openalex.org/W2121382985","https://openalex.org/W2150333845","https://openalex.org/W2155103946","https://openalex.org/W2230120018","https://openalex.org/W2586303492","https://openalex.org/W2592623476","https://openalex.org/W2634549960","https://openalex.org/W2739984154","https://openalex.org/W2917869662","https://openalex.org/W3021722416","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2330640442","https://openalex.org/W1544816068","https://openalex.org/W1975234065","https://openalex.org/W2392533133","https://openalex.org/W2617981106","https://openalex.org/W4251142058","https://openalex.org/W1965041963","https://openalex.org/W2010592405","https://openalex.org/W2370103702","https://openalex.org/W2138146375"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3],"construct":[4],"new":[5],"higher":[6,55],"order":[7,56],"finite":[8,57],"element":[9],"spaces":[10],"for":[11,49],"the":[12,15,30,50],"approximation":[13],"of":[14,32],"two-dimensional":[16],"(2D)":[17],"wave":[18],"equation.":[19],"These":[20,40],"elements":[21],"lead":[22],"to":[23],"explicit":[24],"methods":[25],"after":[26],"time":[27,59],"discretization":[28],"through":[29],"use":[31],"appropriate":[33],"quadrature":[34],"formulas":[35,41],"which":[36],"permit":[37],"mass":[38],"lumping.":[39],"are":[42,47,61,67],"constructed":[43],"explicitly.":[44],"Error":[45],"estimates":[46],"provided":[48],"corresponding":[51],"semidiscrete":[52],"problem.":[53],"Finally,":[54],"difference":[58],"discretizations":[60],"proposed":[62],"and":[63],"various":[64],"numerical":[65],"results":[66],"shown.":[68]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":18},{"year":2017,"cited_by_count":16},{"year":2016,"cited_by_count":15},{"year":2015,"cited_by_count":13},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":15}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
