{"id":"https://openalex.org/W2607785193","doi":"https://doi.org/10.1515/cmam-2017-0041","title":"Combining the DPG Method with Finite Elements","display_name":"Combining the DPG Method with Finite Elements","publication_year":2017,"publication_date":"2017-09-30","ids":{"openalex":"https://openalex.org/W2607785193","doi":"https://doi.org/10.1515/cmam-2017-0041","mag":"2607785193"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2017-0041","is_oa":true,"landing_page_url":"https://doi.org/10.1515/cmam-2017-0041","pdf_url":"http://www.degruyter.com/downloadpdf/j/cmam.2018.18.issue-4/cmam-2017-0041/cmam-2017-0041.xml","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"http://www.degruyter.com/downloadpdf/j/cmam.2018.18.issue-4/cmam-2017-0041/cmam-2017-0041.xml","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012941359","display_name":"Thomas F\u00fchrer","orcid":"https://orcid.org/0000-0001-5034-6593"},"institutions":[{"id":"https://openalex.org/I162148367","display_name":"Pontificia Universidad Cat\u00f3lica de Chile","ror":"https://ror.org/04teye511","country_code":"CL","type":"education","lineage":["https://openalex.org/I162148367"]}],"countries":["CL"],"is_corresponding":true,"raw_author_name":"Thomas F\u00fchrer","raw_affiliation_strings":["Facultad de Matem\u00e1ticas , Pontificia Universidad Cat\u00f3lica de Chile , Avenida Vicu\u00f1a Mackenna 4860 , Santiago , Chile","Facultad de Matem\u00e1ticas, Pontificia Universidad Cat\u00f3lica de Chile, Avenida Vicu\u00f1a Mackenna 4860, Santiago, Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Facultad de Matem\u00e1ticas , Pontificia Universidad Cat\u00f3lica de Chile , Avenida Vicu\u00f1a Mackenna 4860 , Santiago , Chile","institution_ids":["https://openalex.org/I162148367"]},{"raw_affiliation_string":"Facultad de Matem\u00e1ticas, Pontificia Universidad Cat\u00f3lica de Chile, Avenida Vicu\u00f1a Mackenna 4860, Santiago, Chile","institution_ids":["https://openalex.org/I162148367"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005069559","display_name":"Norbert Heuer","orcid":"https://orcid.org/0000-0002-5171-1457"},"institutions":[{"id":"https://openalex.org/I162148367","display_name":"Pontificia Universidad Cat\u00f3lica de Chile","ror":"https://ror.org/04teye511","country_code":"CL","type":"education","lineage":["https://openalex.org/I162148367"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Norbert Heuer","raw_affiliation_strings":["Facultad de Matem\u00e1ticas , Pontificia Universidad Cat\u00f3lica de Chile , Avenida Vicu\u00f1a Mackenna 4860 , Santiago , Chile","Facultad de Matem\u00e1ticas, Pontificia Universidad Cat\u00f3lica de Chile, Avenida Vicu\u00f1a Mackenna 4860, Santiago, Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Facultad de Matem\u00e1ticas , Pontificia Universidad Cat\u00f3lica de Chile , Avenida Vicu\u00f1a Mackenna 4860 , Santiago , Chile","institution_ids":["https://openalex.org/I162148367"]},{"raw_affiliation_string":"Facultad de Matem\u00e1ticas, Pontificia Universidad Cat\u00f3lica de Chile, Avenida Vicu\u00f1a Mackenna 4860, Santiago, Chile","institution_ids":["https://openalex.org/I162148367"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022638379","display_name":"Michael Karkulik","orcid":"https://orcid.org/0009-0007-2001-4433"},"institutions":[{"id":"https://openalex.org/I75778554","display_name":"Federico Santa Mar\u00eda Technical University","ror":"https://ror.org/05510vn56","country_code":"CL","type":"education","lineage":["https://openalex.org/I75778554"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Michael Karkulik","raw_affiliation_strings":["Departamento de Matem\u00e1tica , Universidad T\u00e9cnica Federico Santa Mar\u00eda , Avenida Espa\u00f1a 1680 , Valpara\u00edso , Chile","Departamento de Matem\u00e1tica, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Avenida Espa\u00f1a, 1680, Valpara\u00edso, Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica , Universidad T\u00e9cnica Federico Santa Mar\u00eda , Avenida Espa\u00f1a 1680 , Valpara\u00edso , Chile","institution_ids":["https://openalex.org/I75778554"]},{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Avenida Espa\u00f1a, 1680, Valpara\u00edso, Chile","institution_ids":["https://openalex.org/I75778554"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054855773","display_name":"Rodolfo Rodr\u0131\u0301guez","orcid":"https://orcid.org/0000-0003-1286-7472"},"institutions":[{"id":"https://openalex.org/I172787465","display_name":"University of Concepci\u00f3n","ror":"https://ror.org/0460jpj73","country_code":"CL","type":"education","lineage":["https://openalex.org/I172787465"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Rodolfo Rodr\u00edguez","raw_affiliation_strings":["Departamento de Ingenier\u00eda Matem\u00e1tica and Centro de Investigaci\u00f3n en Ingenier\u00eda Matem\u00e1tica , Universidad de Concepci\u00f3n , Casilla 160-C , Concepci\u00f3n , Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Ingenier\u00eda Matem\u00e1tica and Centro de Investigaci\u00f3n en Ingenier\u00eda Matem\u00e1tica , Universidad de Concepci\u00f3n , Casilla 160-C , Concepci\u00f3n , Chile","institution_ids":["https://openalex.org/I172787465"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5012941359"],"corresponding_institution_ids":["https://openalex.org/I162148367"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04181628,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"4","first_page":"639","last_page":"652"},"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":1.0,"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":1.0,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8339385390281677},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7198206186294556},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7101300954818726},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6708252429962158},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5396374464035034},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5391727685928345},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.5346122980117798},{"id":"https://openalex.org/keywords/petrov\u2013galerkin-method","display_name":"Petrov\u2013Galerkin method","score":0.5321036577224731},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5211270451545715},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.47478076815605164},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4630686342716217},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46164292097091675},{"id":"https://openalex.org/keywords/advection","display_name":"Advection","score":0.4476810097694397},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12015137076377869},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09114614129066467}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8339385390281677},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7198206186294556},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7101300954818726},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6708252429962158},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5396374464035034},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5391727685928345},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5346122980117798},{"id":"https://openalex.org/C2778540877","wikidata":"https://www.wikidata.org/wiki/Q7179155","display_name":"Petrov\u2013Galerkin method","level":3,"score":0.5321036577224731},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5211270451545715},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.47478076815605164},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4630686342716217},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46164292097091675},{"id":"https://openalex.org/C5072599","wikidata":"https://www.wikidata.org/wiki/Q379788","display_name":"Advection","level":2,"score":0.4476810097694397},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12015137076377869},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09114614129066467},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1515/cmam-2017-0041","is_oa":true,"landing_page_url":"https://doi.org/10.1515/cmam-2017-0041","pdf_url":"http://www.degruyter.com/downloadpdf/j/cmam.2018.18.issue-4/cmam-2017-0041/cmam-2017-0041.xml","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1704.07471","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1704.07471","pdf_url":"https://arxiv.org/pdf/1704.07471","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":"","raw_type":"text"},{"id":"mag:2607785193","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1704.07471","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":"doi:10.48550/arxiv.1704.07471","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1704.07471","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:10.1515/cmam-2017-0041","is_oa":true,"landing_page_url":"https://doi.org/10.1515/cmam-2017-0041","pdf_url":"http://www.degruyter.com/downloadpdf/j/cmam.2018.18.issue-4/cmam-2017-0041/cmam-2017-0041.xml","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2499276542","display_name":null,"funder_award_id":"1170672","funder_id":"https://openalex.org/F4320334812","funder_display_name":"Comisi\u00f3n Nacional de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica"},{"id":"https://openalex.org/G5136694873","display_name":null,"funder_award_id":"ACT1118","funder_id":"https://openalex.org/F4320334812","funder_display_name":"Comisi\u00f3n Nacional de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica"},{"id":"https://openalex.org/G5516081612","display_name":null,"funder_award_id":"1150056","funder_id":"https://openalex.org/F4320334812","funder_display_name":"Comisi\u00f3n Nacional de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica"},{"id":"https://openalex.org/G6088053155","display_name":null,"funder_award_id":"PFB-03","funder_id":"https://openalex.org/F4320334812","funder_display_name":"Comisi\u00f3n Nacional de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica"}],"funders":[{"id":"https://openalex.org/F4320334812","display_name":"Comisi\u00f3n Nacional de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica","ror":"https://ror.org/02ap3w078"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1955273710","https://openalex.org/W1973595837","https://openalex.org/W1975941099","https://openalex.org/W1976385614","https://openalex.org/W1992113402","https://openalex.org/W2003453600","https://openalex.org/W2005800036","https://openalex.org/W2013820654","https://openalex.org/W2048846455","https://openalex.org/W2060065779","https://openalex.org/W2086298877","https://openalex.org/W2119759746","https://openalex.org/W2211063485","https://openalex.org/W2322007186","https://openalex.org/W2525918983","https://openalex.org/W2964326343"],"related_works":["https://openalex.org/W2963652791","https://openalex.org/W1976385614","https://openalex.org/W2045162250","https://openalex.org/W2322007186","https://openalex.org/W2949489395","https://openalex.org/W2796629565","https://openalex.org/W2018289994","https://openalex.org/W2963142826","https://openalex.org/W2892312065","https://openalex.org/W3198811363","https://openalex.org/W3040018331","https://openalex.org/W3028365459","https://openalex.org/W2949932653","https://openalex.org/W2039955529","https://openalex.org/W3026351437","https://openalex.org/W2088114223","https://openalex.org/W2917675306","https://openalex.org/W2962736395","https://openalex.org/W2002886035","https://openalex.org/W2152089938"],"abstract_inverted_index":{"Abstract":[0],"We":[1,34,94],"propose":[2,35],"and":[3,13,54,68,79,98],"analyze":[4],"a":[5,36,90],"discretization":[6,63],"scheme":[7],"that":[8,40],"combines":[9],"the":[10,43,59,76,84],"discontinuous":[11],"Petrov\u2013Galerkin":[12],"finite":[14],"element":[15],"methods.":[16],"The":[17],"underlying":[18],"model":[19],"problem":[20],"is":[21,41],"of":[22,42,55],"general":[23],"diffusion-advection-reaction":[24],"type":[25],"on":[26],"bounded":[27],"domains,":[28],"with":[29,47,64],"decomposition":[30],"into":[31],"two":[32],"sub-domains.":[33],"heterogeneous":[37],"variational":[38],"formulation":[39],"ultra-weak":[44,77],"(Petrov\u2013Galerkin)":[45],"form":[46,57],"broken":[48],"test":[49,70,73,81],"space":[50],"in":[51,58],"one":[52],"part,":[53],"Bubnov\u2013Galerkin":[56,85],"other.":[60],"A":[61],"standard":[62,80],"conforming":[65],"approximation":[66],"spaces":[67,71],"appropriate":[69],"(optimal":[72],"functions":[74,82],"for":[75,83],"part":[78],"part)":[86],"gives":[87],"rise":[88],"to":[89],"coupled":[91],"DPG-FEM":[92],"scheme.":[93],"prove":[95],"its":[96],"well-posedness":[97],"quasi-optimal":[99],"convergence.":[100],"Numerical":[101],"results":[102],"confirm":[103],"expected":[104],"convergence":[105],"orders.":[106]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}