{"id":"https://openalex.org/W4316591558","doi":"https://doi.org/10.1007/s10915-022-02087-0","title":"Spectral Analysis of High Order Continuous FEM for Hyperbolic PDEs on Triangular Meshes: Influence of Approximation, Stabilization, and Time-Stepping","display_name":"Spectral Analysis of High Order Continuous FEM for Hyperbolic PDEs on Triangular Meshes: Influence of Approximation, Stabilization, and Time-Stepping","publication_year":2023,"publication_date":"2023-01-21","ids":{"openalex":"https://openalex.org/W4316591558","doi":"https://doi.org/10.1007/s10915-022-02087-0","pmid":"https://pubmed.ncbi.nlm.nih.gov/36699619"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-022-02087-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-022-02087-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-022-02087-0.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10915-022-02087-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068761188","display_name":"Sixtine Michel","orcid":null},"institutions":[{"id":"https://openalex.org/I129235615","display_name":"CEA CESTA","ror":"https://ror.org/026ma2c10","country_code":"FR","type":"government","lineage":["https://openalex.org/I129235615","https://openalex.org/I4210101455"]},{"id":"https://openalex.org/I2738703131","display_name":"Commissariat \u00e0 l'\u00c9nergie Atomique et aux \u00c9nergies Alternatives","ror":"https://ror.org/00jjx8s55","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Sixtine Michel","raw_affiliation_strings":["CEA CESTA, 15 av. des Sabli\u00e8res, 33114 Le Barp, France","CEA CESTA, 15 av. des Sabli\u00e8res, 33114, Le Barp, France"],"affiliations":[{"raw_affiliation_string":"CEA CESTA, 15 av. des Sabli\u00e8res, 33114 Le Barp, France","institution_ids":["https://openalex.org/I2738703131","https://openalex.org/I129235615"]},{"raw_affiliation_string":"CEA CESTA, 15 av. des Sabli\u00e8res, 33114, Le Barp, France","institution_ids":["https://openalex.org/I2738703131","https://openalex.org/I129235615"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001096885","display_name":"Davide Torlo","orcid":"https://orcid.org/0000-0001-5106-1629"},"institutions":[{"id":"https://openalex.org/I138549579","display_name":"Scuola Internazionale Superiore di Studi Avanzati","ror":"https://ror.org/004fze387","country_code":"IT","type":"education","lineage":["https://openalex.org/I138549579"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Davide Torlo","raw_affiliation_strings":["Mathematics Area, SISSA Mathlab, SISSA, via Bonomea, 265, 34136 Trieste, Italy","Mathematics Area, SISSA Mathlab, SISSA, via Bonomea, 265, 34136, Trieste, Italy"],"affiliations":[{"raw_affiliation_string":"Mathematics Area, SISSA Mathlab, SISSA, via Bonomea, 265, 34136 Trieste, Italy","institution_ids":["https://openalex.org/I138549579"]},{"raw_affiliation_string":"Mathematics Area, SISSA Mathlab, SISSA, via Bonomea, 265, 34136, Trieste, Italy","institution_ids":["https://openalex.org/I138549579"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082027942","display_name":"Mario Ricchiuto","orcid":"https://orcid.org/0000-0002-1679-7339"},"institutions":[{"id":"https://openalex.org/I4210131512","display_name":"Centre Inria de l'universit\u00e9 de Bordeaux","ror":"https://ror.org/03tjcj052","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210131512"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mario Ricchiuto","raw_affiliation_strings":["Team CARDAMOM, Inria Bordeaux Sud-Ouest, 200 av. de la Vieille Tour, 33405 Talence, France","Team CARDAMOM, Inria Bordeaux Sud-Ouest, 200 av. de la Vieille Tour, 33405, Talence, France"],"affiliations":[{"raw_affiliation_string":"Team CARDAMOM, Inria Bordeaux Sud-Ouest, 200 av. de la Vieille Tour, 33405 Talence, France","institution_ids":["https://openalex.org/I4210131512"]},{"raw_affiliation_string":"Team CARDAMOM, Inria Bordeaux Sud-Ouest, 200 av. de la Vieille Tour, 33405, Talence, France","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024564342","display_name":"R\u00e9mi Abgrall","orcid":"https://orcid.org/0000-0002-5553-7476"},"institutions":[{"id":"https://openalex.org/I200744771","display_name":"ZHAW Zurich University of Applied Sciences","ror":null,"country_code":"CH","type":null,"lineage":["https://openalex.org/I200744771"]},{"id":"https://openalex.org/I202697423","display_name":"University of Zurich","ror":"https://ror.org/02crff812","country_code":"CH","type":"education","lineage":["https://openalex.org/I202697423"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"R\u00e9mi Abgrall","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Winterthurstrasse 190, 8057 Zurich, Switzerland","Institut f\u00fcr Mathematik, Winterthurstrasse 190, 8057, Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Winterthurstrasse 190, 8057 Zurich, Switzerland","institution_ids":["https://openalex.org/I202697423","https://openalex.org/I200744771"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Winterthurstrasse 190, 8057, Zurich, Switzerland","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5001096885"],"corresponding_institution_ids":["https://openalex.org/I138549579"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.1673,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.7186013,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"94","issue":"3","first_page":"49","last_page":"49"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9991999864578247,"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/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/T12206","display_name":"Vibration and Dynamic Analysis","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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":0.8772494792938232},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.7490454316139221},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.682407557964325},{"id":"https://openalex.org/keywords/time-stepping","display_name":"Time stepping","score":0.5608387589454651},{"id":"https://openalex.org/keywords/hyperbolic-partial-differential-equation","display_name":"Hyperbolic partial differential equation","score":0.47538793087005615},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.463741660118103},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45101243257522583},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4126628339290619},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.3465002775192261},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19650781154632568}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8772494792938232},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.7490454316139221},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.682407557964325},{"id":"https://openalex.org/C3019693144","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Time stepping","level":3,"score":0.5608387589454651},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.47538793087005615},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.463741660118103},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45101243257522583},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4126628339290619},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3465002775192261},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19650781154632568},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":10,"locations":[{"id":"doi:10.1007/s10915-022-02087-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-022-02087-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-022-02087-0.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},{"id":"pmid:36699619","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36699619","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of scientific computing","raw_type":null},{"id":"pmh:oai:www.zora.uzh.ch:229601","is_oa":true,"landing_page_url":"https://www.zora.uzh.ch/id/eprint/229601/1/ZORA_s10915_022_02087_0.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401281","display_name":"Zurich Open Repository and Archive (University of Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I202697423","host_organization_name":"University of Zurich","host_organization_lineage":["https://openalex.org/I202697423"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Michel, Sixtine; Torlo, Davide; Ricchiuto, Mario; Abgrall, Remi  (2023). Spectral Analysis of High Order Continuous FEM for Hyperbolic PDEs on Triangular Meshes: Influence of Approximation, Stabilization, and Time-Stepping.  Journal of Scientific Computing, 94(3):49.","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:2206.06150","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2206.06150","pdf_url":"https://arxiv.org/pdf/2206.06150","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-03940122v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-03940122","pdf_url":"https://inria.hal.science/hal-03940122/document","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Scientific Computing, 2023, 94 (49), &#x27E8;10.1007/s10915-022-02087-0&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:iris.uniroma1.it:11573/1707511","is_oa":true,"landing_page_url":"https://hdl.handle.net/11573/1707511","pdf_url":"https://iris.uniroma1.it/bitstream/11573/1707511/1/Michel_Spectral_2023.pdf","source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pubmedcentral.nih.gov:9867690","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9867690","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC9867690/pdf/10915_2022_Article_2087.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"J Sci Comput","raw_type":"Text"},{"id":"pmh:doi:10.5167/uzh-229601","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:oskar-bordeaux.fr:20.500.12278/190698","is_oa":false,"landing_page_url":"https://oskar-bordeaux.fr/handle/20.500.12278/190698","pdf_url":null,"source":{"id":"https://openalex.org/S4306402569","display_name":"Oskar-Bordeaux (Universite de Bordeaux)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article de revue"},{"id":"doi:10.5167/uzh-229601","is_oa":true,"landing_page_url":"https://doi.org/10.5167/uzh-229601","pdf_url":null,"source":{"id":"https://openalex.org/S7407051291","display_name":"Universit\u00e4t Z\u00fcrich, ZORA","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1007/s10915-022-02087-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-022-02087-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-022-02087-0.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7791736332","display_name":null,"funder_award_id":"200020_175784","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320313934","display_name":"Institut national de recherche en informatique et en automatique (INRIA)","ror":"https://ror.org/02kvxyf05"},{"id":"https://openalex.org/F4320314064","display_name":"Scuola Internazionale Superiore di Studi Avanzati","ror":"https://ror.org/004fze387"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320323731","display_name":"Bureau de Recherches G\u00e9ologiques et Mini\u00e8res","ror":"https://ror.org/05hnb7x64"},{"id":"https://openalex.org/F4320325796","display_name":"Conseil R\u00e9gional Aquitaine","ror":"https://ror.org/01wjxf448"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4316591558.pdf"},"referenced_works_count":56,"referenced_works":["https://openalex.org/W1585098889","https://openalex.org/W1965490868","https://openalex.org/W1970213140","https://openalex.org/W1983036154","https://openalex.org/W2014282047","https://openalex.org/W2027956662","https://openalex.org/W2030213082","https://openalex.org/W2032716933","https://openalex.org/W2039661575","https://openalex.org/W2057880143","https://openalex.org/W2073839654","https://openalex.org/W2073897969","https://openalex.org/W2077661108","https://openalex.org/W2079615698","https://openalex.org/W2091354775","https://openalex.org/W2091914394","https://openalex.org/W2104724067","https://openalex.org/W2128924369","https://openalex.org/W2132133111","https://openalex.org/W2135528904","https://openalex.org/W2139494815","https://openalex.org/W2148445249","https://openalex.org/W2152512756","https://openalex.org/W2174807904","https://openalex.org/W2300432673","https://openalex.org/W2587734875","https://openalex.org/W2612906558","https://openalex.org/W2735613518","https://openalex.org/W2739470739","https://openalex.org/W2768176009","https://openalex.org/W2900682338","https://openalex.org/W2907689018","https://openalex.org/W2912545350","https://openalex.org/W2943918383","https://openalex.org/W2945798956","https://openalex.org/W2963134571","https://openalex.org/W2963700786","https://openalex.org/W2986065419","https://openalex.org/W2996615006","https://openalex.org/W3010292040","https://openalex.org/W3010658891","https://openalex.org/W3089704316","https://openalex.org/W3095903795","https://openalex.org/W3096253157","https://openalex.org/W3100603004","https://openalex.org/W3101776347","https://openalex.org/W3118933647","https://openalex.org/W3155319285","https://openalex.org/W3200699243","https://openalex.org/W3213878575","https://openalex.org/W4206225165","https://openalex.org/W4206447028","https://openalex.org/W4212951453","https://openalex.org/W4241216363","https://openalex.org/W4300797690","https://openalex.org/W4316591558"],"related_works":["https://openalex.org/W2376992165","https://openalex.org/W2784995402","https://openalex.org/W2056259617","https://openalex.org/W3016132316","https://openalex.org/W3174219354","https://openalex.org/W2066764747","https://openalex.org/W161810272","https://openalex.org/W144405564","https://openalex.org/W3118471514","https://openalex.org/W2969693569"],"abstract_inverted_index":{"In":[0],"this":[1],"work":[2],"we":[3,118,135,146],"study":[4,63,83],"various":[5],"continuous":[6,36],"finite":[7],"element":[8],"discretization":[9,45],"for":[10,140,165],"two":[11,122],"dimensional":[12,62],"hyperbolic":[13],"partial":[14],"differential":[15],"equations,":[16],"varying":[17,128],"the":[18,31,43,60,101,114,129,132,138,154,171,204],"polynomial":[19],"space":[20],"(Lagrangian":[21],"on":[22,25,88,121,179],"equispaced,":[23],"Lagrangian":[24],"quadrature":[26],"points":[27],"(<i>Cubature</i>)":[28],"and":[29,42,52,97,104,134,181,184,200],"Bernstein),":[30],"stabilization":[32,105,202],"techniques":[33],"(streamline-upwind":[34],"Petrov-Galerkin,":[35],"interior":[37],"penalty,":[38],"orthogonal":[39],"subscale":[40],"stabilization)":[41],"time":[44,186],"(Runge-Kutta":[46],"(RK),":[47],"strong":[48],"stability":[49,96,143],"preserving":[50],"RK":[51],"deferred":[53],"correction).":[54],"This":[55],"is":[56,203],"an":[57],"extension":[58],"of":[59,91,124,131,167],"one":[61],"by":[64],"Michel":[65],"et":[66],"al.":[67],"(J":[68],"Sci":[69],"Comput":[70],"89(2):31,":[71],"2021.":[72],"10.1007/s10915-021-01632-7),":[73],"whose":[74],"results":[75,139,173],"do":[76],"not":[77],"hold":[78],"in":[79,109,156],"multi-dimensional":[80],"frameworks.":[81],"The":[82,107],"ranks":[84],"these":[85,163],"schemes":[86],"based":[87],"efficiency":[89],"(most":[90],"them":[92],"are":[93,111,174,188],"mass-matrix":[94],"free),":[95],"dispersion":[98],"error,":[99],"providing":[100],"best":[102],"CFL":[103],"coefficients.":[106],"challenges":[108],"two-dimensions":[110],"related":[112],"to":[113,152,158,161],"Fourier":[115],"analysis.":[116,144],"Here,":[117],"perform":[119],"it":[120],"types":[123],"periodic":[125],"triangular":[126],"meshes":[127],"angle":[130],"advection,":[133],"combine":[136],"all":[137],"a":[141],"general":[142],"Furthermore,":[145],"introduce":[147],"additional":[148],"high":[149],"order":[150,157],"viscosity":[151],"stabilize":[153],"discontinuities,":[155],"show":[159],"how":[160],"use":[162],"methods":[164],"tests":[166],"practical":[168],"interest.":[169],"All":[170],"theoretical":[172],"thoroughly":[175],"validated":[176],"numerically":[177],"both":[178],"linear":[180],"non-linear":[182],"problems,":[183],"error-CPU":[185],"curves":[187],"provided.":[189],"Our":[190],"final":[191],"conclusions":[192],"suggest":[193],"that":[194],"<i>Cubature</i>":[195],"elements":[196],"combined":[197],"with":[198],"SSPRK":[199],"OSS":[201],"most":[205],"promising":[206],"combination.":[207]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}