{"id":"https://openalex.org/W3043399409","doi":"https://doi.org/10.1007/s10915-021-01434-x","title":"Stable Filtering Procedures for Nodal Discontinuous Galerkin Methods","display_name":"Stable Filtering Procedures for Nodal Discontinuous Galerkin Methods","publication_year":2021,"publication_date":"2021-02-27","ids":{"openalex":"https://openalex.org/W3043399409","doi":"https://doi.org/10.1007/s10915-021-01434-x","mag":"3043399409"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-021-01434-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-021-01434-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01434-x.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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01434-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057106073","display_name":"Jan Nordstr\u00f6m","orcid":"https://orcid.org/0000-0002-7972-6183"},"institutions":[{"id":"https://openalex.org/I102134673","display_name":"Link\u00f6ping University","ror":"https://ror.org/05ynxx418","country_code":"SE","type":"education","lineage":["https://openalex.org/I102134673"]},{"id":"https://openalex.org/I24027795","display_name":"University of Johannesburg","ror":"https://ror.org/04z6c2n17","country_code":"ZA","type":"education","lineage":["https://openalex.org/I24027795"]}],"countries":["SE","ZA"],"is_corresponding":true,"raw_author_name":"Jan Nordstr\u00f6m","raw_affiliation_strings":["Department of Mathematics and Applied Mathematics, University of Johannesburg, P.O. Box 524, Auckland Park 2006, Johannesburg, South Africa","Department of Mathematics; Computational Mathematics, Link\u00f6ping University, SE-581 83, Link\u00f6ping, Sweden","Link\u00f6ping University"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, University of Johannesburg, P.O. Box 524, Auckland Park 2006, Johannesburg, South Africa","institution_ids":["https://openalex.org/I24027795"]},{"raw_affiliation_string":"Department of Mathematics; Computational Mathematics, Link\u00f6ping University, SE-581 83, Link\u00f6ping, Sweden","institution_ids":["https://openalex.org/I102134673"]},{"raw_affiliation_string":"Link\u00f6ping University","institution_ids":["https://openalex.org/I102134673"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072910798","display_name":"Andrew R. Winters","orcid":"https://orcid.org/0000-0002-5902-1522"},"institutions":[{"id":"https://openalex.org/I102134673","display_name":"Link\u00f6ping University","ror":"https://ror.org/05ynxx418","country_code":"SE","type":"education","lineage":["https://openalex.org/I102134673"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Andrew R. Winters","raw_affiliation_strings":["Department of Mathematics; Computational Mathematics, Link\u00f6ping University, SE-581 83, Link\u00f6ping, Sweden","Link\u00f6ping University"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics; Computational Mathematics, Link\u00f6ping University, SE-581 83, Link\u00f6ping, Sweden","institution_ids":["https://openalex.org/I102134673"]},{"raw_affiliation_string":"Link\u00f6ping University","institution_ids":["https://openalex.org/I102134673"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057106073"],"corresponding_institution_ids":["https://openalex.org/I102134673","https://openalex.org/I24027795"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00773732,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"87","issue":"1","first_page":null,"last_page":null},"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":0.9997000098228455,"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":0.9997000098228455,"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":0.9997000098228455,"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/T12727","display_name":"Differential Equations and Numerical Methods","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"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7651549577713013},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6830853223800659},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6458716988563538},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.6114463210105896},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.5777766704559326},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.5665408372879028},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.5476965308189392},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5475661158561707},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4949881434440613},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4366295635700226},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.41918838024139404},{"id":"https://openalex.org/keywords/gauss","display_name":"Gauss","score":0.4138326644897461},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3235470652580261},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.23656997084617615},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20517674088478088},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.17869612574577332},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.06739670038223267}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7651549577713013},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6830853223800659},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6458716988563538},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.6114463210105896},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.5777766704559326},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5665408372879028},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.5476965308189392},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5475661158561707},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4949881434440613},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4366295635700226},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.41918838024139404},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.4138326644897461},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3235470652580261},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.23656997084617615},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20517674088478088},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.17869612574577332},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.06739670038223267},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10915-021-01434-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-021-01434-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01434-x.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":"pmh:oai:arXiv.org:2007.06948","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.06948","pdf_url":"https://arxiv.org/pdf/2007.06948","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":"mag:3043399409","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/2007.06948.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:DiVA.org:liu-173682","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-173682","pdf_url":null,"source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article in journal"},{"id":"doi:10.48550/arxiv.2007.06948","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2007.06948","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10915-021-01434-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-021-01434-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01434-x.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/G7790445587","display_name":null,"funder_award_id":"2018-05084 VR","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"}],"funders":[{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3043399409.pdf","grobid_xml":"https://content.openalex.org/works/W3043399409.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W96454744","https://openalex.org/W159877182","https://openalex.org/W830650959","https://openalex.org/W1583515859","https://openalex.org/W1583892864","https://openalex.org/W1627568958","https://openalex.org/W1972670182","https://openalex.org/W1975229625","https://openalex.org/W1986328299","https://openalex.org/W1987377268","https://openalex.org/W2002083525","https://openalex.org/W2010222530","https://openalex.org/W2017727977","https://openalex.org/W2031567600","https://openalex.org/W2041145218","https://openalex.org/W2049068370","https://openalex.org/W2049991352","https://openalex.org/W2053425018","https://openalex.org/W2079635318","https://openalex.org/W2091121763","https://openalex.org/W2093745318","https://openalex.org/W2095039621","https://openalex.org/W2133867538","https://openalex.org/W2343405662","https://openalex.org/W2528000392","https://openalex.org/W2560142783","https://openalex.org/W2769562095","https://openalex.org/W2949414414","https://openalex.org/W3000339403","https://openalex.org/W3044301758","https://openalex.org/W4205236375","https://openalex.org/W4247375400","https://openalex.org/W4251197584","https://openalex.org/W6602227077"],"related_works":["https://openalex.org/W2557648111","https://openalex.org/W1602579916","https://openalex.org/W2186977505","https://openalex.org/W3164504707","https://openalex.org/W2008031894","https://openalex.org/W3122973256","https://openalex.org/W2033313052","https://openalex.org/W1943706693","https://openalex.org/W2892158442","https://openalex.org/W3160875901","https://openalex.org/W2282978183","https://openalex.org/W2338655423","https://openalex.org/W2159399125","https://openalex.org/W2904532103","https://openalex.org/W1527588020","https://openalex.org/W2955969013","https://openalex.org/W2093066650","https://openalex.org/W3106385364","https://openalex.org/W2471199666","https://openalex.org/W2070144563"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"prove":[2],"that":[3,20,31],"the":[4,21,52,60],"most":[5],"common":[6],"filtering":[7,45],"procedure":[8],"for":[9,47],"nodal":[10],"discontinuous":[11],"Galerkin":[12],"(DG)":[13],"methods":[14,50],"is":[15,24],"stable.":[16],"The":[17,40],"proof":[18],"exploits":[19],"DG":[22,53],"approximation":[23],"constructed":[25],"from":[26],"polynomial":[27],"basis":[28],"functions":[29],"and":[30,58],"integrals":[32],"are":[33],"approximated":[34],"with":[35],"high-order":[36],"accurate":[37],"Legendre\u2013Gauss\u2013Lobatto":[38],"quadrature.":[39],"theoretical":[41,62],"discussion":[42],"re-contextualizes":[43],"stable":[44],"results":[46],"finite":[48],"difference":[49],"into":[51],"setting.":[54],"Numerical":[55],"tests":[56],"verify":[57],"validate":[59],"underlying":[61],"results.":[63]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}