{"id":"https://openalex.org/W2622581481","doi":"https://doi.org/10.1515/cmam-2017-0011","title":"On Finite Element Formulations for the Obstacle Problem \u2013 Mixed and Stabilised Methods","display_name":"On Finite Element Formulations for the Obstacle Problem \u2013 Mixed and Stabilised Methods","publication_year":2017,"publication_date":"2017-06-08","ids":{"openalex":"https://openalex.org/W2622581481","doi":"https://doi.org/10.1515/cmam-2017-0011","mag":"2622581481"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2017-0011","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2017-0011","pdf_url":null,"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":"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/A5023168269","display_name":"Tom Gustafsson","orcid":"https://orcid.org/0000-0003-1611-5032"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Tom Gustafsson","raw_affiliation_strings":["Department of Mathematics and Systems Analysis , Aalto University School of Science , Espoo , Finland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Systems Analysis , Aalto University School of Science , Espoo , Finland","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006069937","display_name":"Rolf Stenberg","orcid":"https://orcid.org/0000-0001-9012-2754"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Rolf Stenberg","raw_affiliation_strings":["Department of Mathematics and Systems Analysis , Aalto University School of Science , Espoo , Finland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Systems Analysis , Aalto University School of Science , Espoo , Finland","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067441095","display_name":"Juha Videman","orcid":"https://orcid.org/0000-0001-8194-1635"},"institutions":[{"id":"https://openalex.org/I141596103","display_name":"University of Lisbon","ror":"https://ror.org/01c27hj86","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103"]},{"id":"https://openalex.org/I203847022","display_name":"Instituto Polit\u00e9cnico de Lisboa","ror":"https://ror.org/04ea70f07","country_code":"PT","type":"education","lineage":["https://openalex.org/I203847022"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Juha Videman","raw_affiliation_strings":["Department of Mathematics , Instituto Superior T\u00e9cnico, Universidade de Lisboa , Lisboa , Portugal"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Instituto Superior T\u00e9cnico, Universidade de Lisboa , Lisboa , Portugal","institution_ids":["https://openalex.org/I203847022","https://openalex.org/I141596103"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5006069937"],"corresponding_institution_ids":["https://openalex.org/I9927081"],"apc_list":null,"apc_paid":null,"fwci":0.9604,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.72734207,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"17","issue":"3","first_page":"413","last_page":"429"},"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":0.9994999766349792,"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":0.9994999766349792,"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":0.9973000288009644,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9958999752998352,"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/finite-element-method","display_name":"Finite element method","score":0.8163893222808838},{"id":"https://openalex.org/keywords/obstacle","display_name":"Obstacle","score":0.8106656074523926},{"id":"https://openalex.org/keywords/obstacle-problem","display_name":"Obstacle problem","score":0.7736668586730957},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.5938646197319031},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5524291396141052},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5453812479972839},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.5059992671012878},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.47969695925712585},{"id":"https://openalex.org/keywords/extended-finite-element-method","display_name":"Extended finite element method","score":0.42359888553619385},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42150717973709106},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3579323887825012},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.18078672885894775},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.129774272441864},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.09576520323753357}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.8163893222808838},{"id":"https://openalex.org/C2776650193","wikidata":"https://www.wikidata.org/wiki/Q264661","display_name":"Obstacle","level":2,"score":0.8106656074523926},{"id":"https://openalex.org/C132369183","wikidata":"https://www.wikidata.org/wiki/Q3406250","display_name":"Obstacle problem","level":3,"score":0.7736668586730957},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.5938646197319031},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5524291396141052},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5453812479972839},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.5059992671012878},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.47969695925712585},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.42359888553619385},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42150717973709106},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3579323887825012},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.18078672885894775},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.129774272441864},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09576520323753357},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2017-0011","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2017-0011","pdf_url":null,"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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4699999988079071,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G7903421656","display_name":null,"funder_award_id":"3305/31/2015","funder_id":"https://openalex.org/F4320321855","funder_display_name":"Tekes"}],"funders":[{"id":"https://openalex.org/F4320321855","display_name":"Tekes","ror":"https://ror.org/02ag8cq23"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W581038412","https://openalex.org/W606079047","https://openalex.org/W1513782764","https://openalex.org/W1536407545","https://openalex.org/W1600143726","https://openalex.org/W1708679080","https://openalex.org/W1778185943","https://openalex.org/W1855073313","https://openalex.org/W1967077838","https://openalex.org/W1985822578","https://openalex.org/W1986608219","https://openalex.org/W1989895848","https://openalex.org/W2015148405","https://openalex.org/W2026365342","https://openalex.org/W2029129352","https://openalex.org/W2030580548","https://openalex.org/W2031407958","https://openalex.org/W2033736734","https://openalex.org/W2035781708","https://openalex.org/W2044627846","https://openalex.org/W2048166110","https://openalex.org/W2062002217","https://openalex.org/W2079423956","https://openalex.org/W2094792403","https://openalex.org/W2121989547","https://openalex.org/W2128049218","https://openalex.org/W2156173979","https://openalex.org/W2520982264","https://openalex.org/W2952975292","https://openalex.org/W3000757360","https://openalex.org/W3102985974","https://openalex.org/W4210300254","https://openalex.org/W4231269780","https://openalex.org/W4301283118"],"related_works":["https://openalex.org/W2368569380","https://openalex.org/W1989743438","https://openalex.org/W4226485513","https://openalex.org/W1993397232","https://openalex.org/W1482810786","https://openalex.org/W1979757175","https://openalex.org/W4238417450","https://openalex.org/W2781836279","https://openalex.org/W2005894392","https://openalex.org/W2204764070"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"discuss":[2],"the":[3,6,13,18,25],"differences":[4],"between":[5],"penalty,":[7],"mixed":[8],"and":[9,29],"stabilised":[10],"methods":[11,26],"for":[12],"finite":[14],"element":[15],"approximation":[16],"of":[17,24],"obstacle":[19],"problem.":[20],"The":[21],"theoretical":[22],"properties":[23],"are":[27],"discussed":[28],"illustrated":[30],"through":[31],"numerical":[32],"examples.":[33]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}