{"id":"https://openalex.org/W2069555630","doi":"https://doi.org/10.1090/s0025-5718-2010-02364-6","title":"A two-level enriched finite element method for a mixed problem","display_name":"A two-level enriched finite element method for a mixed problem","publication_year":2010,"publication_date":"2010-07-26","ids":{"openalex":"https://openalex.org/W2069555630","doi":"https://doi.org/10.1090/s0025-5718-2010-02364-6","mag":"2069555630"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2010-02364-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2010-02364-6","pdf_url":"https://www.ams.org/mcom/2011-80-273/S0025-5718-2010-02364-6/S0025-5718-2010-02364-6.pdf","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","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":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2011-80-273/S0025-5718-2010-02364-6/S0025-5718-2010-02364-6.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015733916","display_name":"Alejandro Allendes","orcid":"https://orcid.org/0000-0002-3305-6823"},"institutions":[{"id":"https://openalex.org/I181647926","display_name":"University of Strathclyde","ror":"https://ror.org/00n3w3b69","country_code":"GB","type":"education","lineage":["https://openalex.org/I181647926"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Alejandro Allendes","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, United Kingdom","Mathematics And Statistics"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, United Kingdom","institution_ids":["https://openalex.org/I181647926"]},{"raw_affiliation_string":"Mathematics And Statistics","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025324947","display_name":"Gabriel R. Barrenechea","orcid":"https://orcid.org/0000-0003-4490-678X"},"institutions":[{"id":"https://openalex.org/I181647926","display_name":"University of Strathclyde","ror":"https://ror.org/00n3w3b69","country_code":"GB","type":"education","lineage":["https://openalex.org/I181647926"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Gabriel Barrenechea","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, United Kingdom","Mathematics And Statistics"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, United Kingdom","institution_ids":["https://openalex.org/I181647926"]},{"raw_affiliation_string":"Mathematics And Statistics","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047900709","display_name":"Erwin Hern\u00e1ndez","orcid":"https://orcid.org/0000-0002-0821-4658"},"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":"Erwin Hern\u00e1ndez","raw_affiliation_strings":["Departamento de Matem\u00c3\u00a1tica, Universidad T\u00c3\u00a9cnica Federico Santa Mar\u00c3\u00ada, Casilla 110-V, Valpara\u00c3\u00adso, Chile","Departamento de Matem\u00e1tica , Universidad T\u00e9cnica Federico Santa Mar\u00eda , Casilla 110-V, Valpara\u00edso , Chile"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00c3\u00a1tica, Universidad T\u00c3\u00a9cnica Federico Santa Mar\u00c3\u00ada, Casilla 110-V, Valpara\u00c3\u00adso, Chile","institution_ids":[]},{"raw_affiliation_string":"Departamento de Matem\u00e1tica , Universidad T\u00e9cnica Federico Santa Mar\u00eda , Casilla 110-V, Valpara\u00edso , Chile","institution_ids":["https://openalex.org/I75778554"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059362886","display_name":"Fr\u00e9d\u00e9ric Valentin","orcid":"https://orcid.org/0000-0002-5056-7529"},"institutions":[{"id":"https://openalex.org/I4210142352","display_name":"Laborat\u00f3rio Nacional de Computa\u00e7\u00e3o Cient\u00edfica","ror":"https://ror.org/0498ekt05","country_code":"BR","type":"government","lineage":["https://openalex.org/I4210142352"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9ric Valentin","raw_affiliation_strings":["Departamento de Matem\u00c3\u00a1tica Aplicada e Computacional, Laborat\u00c3\u00b3rio Nacional de Computa\u00c3\u00a7\u00c3\u00a3o Cient\u00c3\u00adfica, Av. Get\u00c3\u00balio Vargas, 333, 25651-070 Petr\u00c3\u00b3polis - RJ, Brazil","Laborat\u00f3rio Nacional de Computa\u00e7\u00e3o Cient\u00edfica"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00c3\u00a1tica Aplicada e Computacional, Laborat\u00c3\u00b3rio Nacional de Computa\u00c3\u00a7\u00c3\u00a3o Cient\u00c3\u00adfica, Av. Get\u00c3\u00balio Vargas, 333, 25651-070 Petr\u00c3\u00b3polis - RJ, Brazil","institution_ids":["https://openalex.org/I4210142352"]},{"raw_affiliation_string":"Laborat\u00f3rio Nacional de Computa\u00e7\u00e3o Cient\u00edfica","institution_ids":["https://openalex.org/I4210142352"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5015733916"],"corresponding_institution_ids":["https://openalex.org/I181647926"],"apc_list":null,"apc_paid":null,"fwci":1.0298,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.78355254,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"80","issue":"273","first_page":"11","last_page":"41"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9994999766349792,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8730090856552124},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7842658162117004},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7725626230239868},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.5579596161842346},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.5347926020622253},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5248232483863831},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.4943056106567383},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4878838062286377},{"id":"https://openalex.org/keywords/extended-finite-element-method","display_name":"Extended finite element method","score":0.4656883478164673},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4627670347690582},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4511139690876007},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.4493992328643799},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43644940853118896},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.4159236550331116},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2021271288394928},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.07385897636413574},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0672886073589325}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8730090856552124},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7842658162117004},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7725626230239868},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.5579596161842346},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.5347926020622253},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5248232483863831},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.4943056106567383},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4878838062286377},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.4656883478164673},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4627670347690582},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4511139690876007},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.4493992328643799},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43644940853118896},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.4159236550331116},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2021271288394928},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.07385897636413574},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0672886073589325},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0025-5718-2010-02364-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2010-02364-6","pdf_url":"https://www.ams.org/mcom/2011-80-273/S0025-5718-2010-02364-6/S0025-5718-2010-02364-6.pdf","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:strathprints.strath.ac.uk:29059","is_oa":true,"landing_page_url":"https://strathprints.strath.ac.uk/view/author/646837.html>","pdf_url":"https://strathprints.strath.ac.uk/29059/1/a_two_level_enriched_finite_element.pdf","source":{"id":"https://openalex.org/S4306402226","display_name":"Strathprints: The University of Strathclyde institutional repository (University of Strathclyde)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I181647926","host_organization_name":"University of Strathclyde","host_organization_lineage":["https://openalex.org/I181647926"],"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":"PeerReviewed"},{"id":"pmh:oai:americanae.aecid.es:3333996","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3333996","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","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":"MATHEMATICS OF COMPUTATION","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:localhost:10533/133926","is_oa":true,"landing_page_url":"http://hdl.handle.net/10533/133926","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"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":"MATHEMATICS OF COMPUTATION","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2010-02364-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2010-02364-6","pdf_url":"https://www.ams.org/mcom/2011-80-273/S0025-5718-2010-02364-6/S0025-5718-2010-02364-6.pdf","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7900000214576721,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G1840770272","display_name":null,"funder_award_id":"E-26/","funder_id":"https://openalex.org/F4320322749","funder_display_name":"Funda\u00e7\u00e3o Carlos Chagas Filho de Amparo \u00e0 Pesquisa do Estado do Rio de Janeiro"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320322749","display_name":"Funda\u00e7\u00e3o Carlos Chagas Filho de Amparo \u00e0 Pesquisa do Estado do Rio de Janeiro","ror":"https://ror.org/03kk0s825"},{"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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2069555630.pdf","grobid_xml":"https://content.openalex.org/works/W2069555630.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W26249965","https://openalex.org/W125509687","https://openalex.org/W136185420","https://openalex.org/W1601728065","https://openalex.org/W1674659126","https://openalex.org/W1973590664","https://openalex.org/W1974006019","https://openalex.org/W1976509668","https://openalex.org/W1977399978","https://openalex.org/W1997640799","https://openalex.org/W2005788407","https://openalex.org/W2011078493","https://openalex.org/W2041589227","https://openalex.org/W2046002450","https://openalex.org/W2061148553","https://openalex.org/W2067208724","https://openalex.org/W2073263351","https://openalex.org/W2078045751","https://openalex.org/W2084718774","https://openalex.org/W2094442825","https://openalex.org/W2123597308","https://openalex.org/W2155879256","https://openalex.org/W2156609537","https://openalex.org/W2199169705","https://openalex.org/W2519971170","https://openalex.org/W3149667697","https://openalex.org/W6600459194","https://openalex.org/W6605310286","https://openalex.org/W6607890348","https://openalex.org/W6636093862","https://openalex.org/W6813285973"],"related_works":["https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W1977906733","https://openalex.org/W2047719014","https://openalex.org/W1567939749","https://openalex.org/W2040975642","https://openalex.org/W2010821947","https://openalex.org/W4234008889","https://openalex.org/W2927373829","https://openalex.org/W1573186872"],"abstract_inverted_index":{"The":[0,62,95,148],"simplest":[1],"pair":[2],"of":[3,58,107,109],"spaces":[4,71],"<inline-formula":[5],"content-type=\"math/mathml\">":[6],"<mml:math":[7],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[8],"alttext=\"double-struck":[9],"upper":[10,15],"P":[11,16],"1":[12],"slash":[13],"double-struck":[14],"0\">":[17],"<mml:semantics>":[18],"<mml:mrow>":[19],"<mml:msub>":[20,32],"<mml:mrow":[21,28,33],"class=\"MJX-TeXAtom-ORD\">":[22,29,34],"<mml:mi":[23,35],"mathvariant=\"double-struck\">P</mml:mi>":[24,36],"</mml:mrow>":[25,31,37,40],"<mml:mn>1</mml:mn>":[26],"</mml:msub>":[27,39],"<mml:mo>/</mml:mo>":[30],"<mml:mn>0</mml:mn>":[38],"<mml:annotation":[41],"encoding=\"application/x-tex\">\\mathbb":[42],"{P}_1":[43],"/":[44],"\\mathbb":[45],"{P}_0</mml:annotation>":[46],"</mml:semantics>":[47],"</mml:math>":[48],"</inline-formula>":[49],"is":[50,65,98,140,162],"made":[51],"inf-sup":[52],"stable":[53],"for":[54],"the":[55,59,68,89,105,110,165,174,186],"mixed":[56],"form":[57],"Darcy":[60,81],"equation.":[61],"key":[63],"ingredient":[64],"to":[66,142],"enhance":[67],"finite":[69,137],"element":[70,138],"inside":[72],"a":[73,133,152],"Petrov-Galerkin":[74],"framework":[75],"with":[76,83,185],"functions":[77],"satisfying":[78],"element-wise":[79],"local":[80,117],"problems":[82],"right":[84],"hand":[85],"sides":[86],"depending":[87],"on":[88,151],"residuals":[90],"over":[91],"elements":[92],"and":[93,103,121,125,156,160,177],"edges.":[94],"enriched":[96],"method":[97,139],"symmetric,":[99],"locally":[100],"mass":[101],"conservative":[102],"keeps":[104],"degrees":[106],"freedom":[108],"original":[111],"interpolation":[112],"spaces.":[113],"First,":[114],"we":[115,122],"assume":[116],"enrichments":[118],"exactly":[119],"computed":[120],"prove":[123],"uniqueness":[124],"optimal":[126],"error":[127],"estimates":[128],"in":[129,180],"natural":[130],"norms.":[131],"Then,":[132],"low":[134],"cost":[135],"two-level":[136],"proposed":[141],"effectively":[143],"obtain":[144],"enhancing":[145],"basis":[146],"functions.":[147],"approach":[149],"lays":[150],"two-scale":[153],"numerical":[154,168,171],"analysis":[155],"shows":[157],"that":[158],"well-posedness":[159],"optimality":[161],"kept,":[163],"despite":[164],"second":[166],"level":[167],"approximation.":[169],"Several":[170],"experiments":[172],"validate":[173],"theoretical":[175],"results":[176,184],"compares":[178],"(favourably":[179],"some":[181],"cases)":[182],"our":[183],"classical":[187],"Raviart-Thomas":[188],"element.":[189]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}