{"id":"https://openalex.org/W2015491166","doi":"https://doi.org/10.1007/s00211-010-0347-y","title":"Finite element approximation of the Sobolev constant","display_name":"Finite element approximation of the Sobolev constant","publication_year":2010,"publication_date":"2010-12-14","ids":{"openalex":"https://openalex.org/W2015491166","doi":"https://doi.org/10.1007/s00211-010-0347-y","mag":"2015491166"},"language":"de","primary_location":{"id":"doi:10.1007/s00211-010-0347-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-010-0347-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","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/A5063675442","display_name":"Paola F. Antonietti","orcid":"https://orcid.org/0000-0002-2138-3878"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Paola F. Antonietti","raw_affiliation_strings":["MOX\u2014Modellistica e Calcolo Scientifico, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy","Politecnico di Milano, MOX\u2014Modellistica e Calcolo Scientifico, Dipartimento di Matematica, Piazza Leonardo da Vinci 32, 20133, Milano, Italy#TAB#"],"affiliations":[{"raw_affiliation_string":"MOX\u2014Modellistica e Calcolo Scientifico, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"Politecnico di Milano, MOX\u2014Modellistica e Calcolo Scientifico, Dipartimento di Matematica, Piazza Leonardo da Vinci 32, 20133, Milano, Italy#TAB#","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103154635","display_name":"Aldo Pratelli","orcid":"https://orcid.org/0000-0002-3670-6625"},"institutions":[{"id":"https://openalex.org/I25217355","display_name":"University of Pavia","ror":"https://ror.org/00s6t1f81","country_code":"IT","type":"education","lineage":["https://openalex.org/I25217355"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Aldo Pratelli","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00e0 di Pavia, via Ferrata 1, 27100, Pavia, Italy","Universita di Pavia, Dipartimento di matematica, via Ferrata 1, 27100, Pavia, Italy#TAB#"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 di Pavia, via Ferrata 1, 27100, Pavia, Italy","institution_ids":["https://openalex.org/I25217355"]},{"raw_affiliation_string":"Universita di Pavia, Dipartimento di matematica, via Ferrata 1, 27100, Pavia, Italy#TAB#","institution_ids":["https://openalex.org/I25217355"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5063675442"],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.346,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.62927672,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"117","issue":"1","first_page":"37","last_page":"64"},"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":0.9993000030517578,"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":0.9993000030517578,"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":0.9991999864578247,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9987000226974487,"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/mathematics","display_name":"Mathematics","score":0.8786792755126953},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.7941961288452148},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6861613988876343},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6261609792709351},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.586524248123169},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.58491450548172},{"id":"https://openalex.org/keywords/unit-sphere","display_name":"Unit sphere","score":0.5783177018165588},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5726770162582397},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.5325518846511841},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4854067265987396},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.46772682666778564},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34394338726997375},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08933570981025696}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8786792755126953},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.7941961288452148},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6861613988876343},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6261609792709351},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.586524248123169},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.58491450548172},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.5783177018165588},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5726770162582397},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.5325518846511841},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4854067265987396},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.46772682666778564},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34394338726997375},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08933570981025696},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00211-010-0347-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-010-0347-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:arpi.unipi.it:11568/1037728","is_oa":false,"landing_page_url":"http://hdl.handle.net/11568/1037728","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:re.public.polimi.it:11311/575322","is_oa":false,"landing_page_url":"http://hdl.handle.net/11311/575322","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1492326914","https://openalex.org/W1550621289","https://openalex.org/W1599696556","https://openalex.org/W1674369032","https://openalex.org/W1970600620","https://openalex.org/W1980183964","https://openalex.org/W2016859302","https://openalex.org/W2017437908","https://openalex.org/W2023227586","https://openalex.org/W2041523977","https://openalex.org/W2050005024","https://openalex.org/W2118387305","https://openalex.org/W2155061016","https://openalex.org/W2562800485","https://openalex.org/W4212992529","https://openalex.org/W4292166829"],"related_works":["https://openalex.org/W4299978068","https://openalex.org/W2016092567","https://openalex.org/W2950745223","https://openalex.org/W2164189677","https://openalex.org/W2387072865","https://openalex.org/W2804455714","https://openalex.org/W1982675504","https://openalex.org/W2048403683","https://openalex.org/W1530081058","https://openalex.org/W2989846825"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}