{"id":"https://openalex.org/W1989743438","doi":"https://doi.org/10.1080/00207169808804710","title":"Numerical solutions of third-order obstacle problems","display_name":"Numerical solutions of third-order obstacle problems","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W1989743438","doi":"https://doi.org/10.1080/00207169808804710","mag":"1989743438"},"language":"en","primary_location":{"id":"doi:10.1080/00207169808804710","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169808804710","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/123456789/12805","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111752781","display_name":"Eisa Al-Said","orcid":null},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Eisa A. Al-Said","raw_affiliation_strings":["Mathematics Department , College of Science, King Saud University , P.O. Box 2455, Riyadh, 11451,  Saudi Arabia","Mathematics Department,  College of Science, King Saud University, P.O. Box 2455,  Riyadh 11451, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department , College of Science, King Saud University , P.O. Box 2455, Riyadh, 11451,  Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]},{"raw_affiliation_string":"Mathematics Department,  College of Science, King Saud University, P.O. Box 2455,  Riyadh 11451, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087578803","display_name":"Muhammad Aslam Noor","orcid":"https://orcid.org/0000-0001-6105-2435"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"M. Aslam Noor","raw_affiliation_strings":["Mathematics Department , College of Science, King Saud University , P.O. Box 2455, Riyadh, 11451,  Saudi Arabia","Mathematics Department,  College of Science, King Saud University, P.O. Box 2455,  Riyadh 11451, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department , College of Science, King Saud University , P.O. Box 2455, Riyadh, 11451,  Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]},{"raw_affiliation_string":"Mathematics Department,  College of Science, King Saud University, P.O. Box 2455,  Riyadh 11451, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111732316","display_name":"Th. M. Rassias","orcid":null},"institutions":[{"id":"https://openalex.org/I174458059","display_name":"National Technical University of Athens","ror":"https://ror.org/03cx6bg69","country_code":"GR","type":"education","lineage":["https://openalex.org/I174458059"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Th. M. Rassias","raw_affiliation_strings":["Mathematics Department , National Technical University of Athens , Zogrofou Campus, Athens, 15773,  Greece","Mathematics Department , National Technical University of Athens , Zogrofou Campus, Athens, 15773, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department , National Technical University of Athens , Zogrofou Campus, Athens, 15773,  Greece","institution_ids":["https://openalex.org/I174458059"]},{"raw_affiliation_string":"Mathematics Department , National Technical University of Athens , Zogrofou Campus, Athens, 15773, Greece","institution_ids":["https://openalex.org/I174458059"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5302,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.81503393,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"69","issue":"1-2","first_page":"75","last_page":"84"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","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"}},"topics":[{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","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/T10545","display_name":"Optimization and Variational Analysis","score":0.9944000244140625,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9815000295639038,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/obstacle","display_name":"Obstacle","score":0.9490126371383667},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.915064811706543},{"id":"https://openalex.org/keywords/obstacle-problem","display_name":"Obstacle problem","score":0.8899828195571899},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7362784147262573},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6243749856948853},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6192759275436401},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5128953456878662},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4549034833908081},{"id":"https://openalex.org/keywords/third-order","display_name":"Third order","score":0.43376410007476807},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40980011224746704},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3317089080810547},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15101870894432068},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.04844895005226135}],"concepts":[{"id":"https://openalex.org/C2776650193","wikidata":"https://www.wikidata.org/wiki/Q264661","display_name":"Obstacle","level":2,"score":0.9490126371383667},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.915064811706543},{"id":"https://openalex.org/C132369183","wikidata":"https://www.wikidata.org/wiki/Q3406250","display_name":"Obstacle problem","level":3,"score":0.8899828195571899},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7362784147262573},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6243749856948853},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6192759275436401},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5128953456878662},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4549034833908081},{"id":"https://openalex.org/C2777566824","wikidata":"https://www.wikidata.org/wiki/Q1259252","display_name":"Third order","level":2,"score":0.43376410007476807},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40980011224746704},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3317089080810547},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15101870894432068},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.04844895005226135},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207169808804710","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169808804710","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:dspace.lib.ntua.gr:123456789/12805","is_oa":true,"landing_page_url":"http://hdl.handle.net/123456789/12805","pdf_url":null,"source":{"id":"https://openalex.org/S4377196837","display_name":"DSpace - NTUA (National Technical University of Athens)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I174458059","host_organization_name":"National Technical University of Athens","host_organization_lineage":["https://openalex.org/I174458059"],"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":"International Journal of Computer Mathematics","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:dspace.lib.ntua.gr:123456789/12805","is_oa":true,"landing_page_url":"http://hdl.handle.net/123456789/12805","pdf_url":null,"source":{"id":"https://openalex.org/S4377196837","display_name":"DSpace - NTUA (National Technical University of Athens)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I174458059","host_organization_name":"National Technical University of Athens","host_organization_lineage":["https://openalex.org/I174458059"],"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":"International Journal of Computer Mathematics","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"display_name":"Life below water","id":"https://metadata.un.org/sdg/14","score":0.6800000071525574}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W404836453","https://openalex.org/W1516681311","https://openalex.org/W1969675363","https://openalex.org/W1973356945","https://openalex.org/W1986074636","https://openalex.org/W1986433866","https://openalex.org/W2004326643","https://openalex.org/W2010462593","https://openalex.org/W2011875845","https://openalex.org/W2013490212","https://openalex.org/W2015562476","https://openalex.org/W2050088224","https://openalex.org/W2064176740","https://openalex.org/W2078644288","https://openalex.org/W2325513961","https://openalex.org/W2524522610","https://openalex.org/W2790980361","https://openalex.org/W4200153169","https://openalex.org/W4234028290"],"related_works":["https://openalex.org/W1989743438","https://openalex.org/W1993397232","https://openalex.org/W4238417450","https://openalex.org/W1482810786","https://openalex.org/W1969086070","https://openalex.org/W4253224454","https://openalex.org/W107811838","https://openalex.org/W2998793487","https://openalex.org/W4308703440","https://openalex.org/W171600397"],"abstract_inverted_index":{"It":[0],"is":[1,64],"known":[2],"that":[3,29],"a":[4,41],"class":[5],"of":[6,20,43],"odd":[7],"order":[8],"obstacle":[9,35],"problems":[10,36],"in":[11,17],"physical":[12],"oceanography":[13],"can":[14,37],"be":[15,38],"studied":[16],"the":[18],"framework":[19],"variational":[21,30,44],"inequality":[22],"theory.":[23],"In":[24],"this":[25],"paper,":[26],"we":[27],"show":[28],"inequalities":[31],"related":[32],"with":[33],"third-order":[34],"characterized":[39],"by":[40],"system":[42],"equations":[45],"without":[46],"constraints,":[47],"which":[48],"are":[49],"solved":[50],"using":[51],"modified":[52],"finite":[53],"difference":[54],"technique.":[55],"A":[56],"comparison":[57],"between":[58],"our":[59],"and":[60],"other":[61],"available":[62],"results":[63],"also":[65],"presented.":[66]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
