{"id":"https://openalex.org/W1980225330","doi":"https://doi.org/10.1155/2012/962070","title":"Discrete Mixed Petrov-Galerkin Finite Element Method for a Fourth-Order Two-Point Boundary Value Problem","display_name":"Discrete Mixed Petrov-Galerkin Finite Element Method for a Fourth-Order Two-Point Boundary Value Problem","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1980225330","doi":"https://doi.org/10.1155/2012/962070","mag":"1980225330"},"language":"en","primary_location":{"id":"doi:10.1155/2012/962070","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2012/962070","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/962070.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2012/962070.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077604862","display_name":"L. Jones Tarcius Doss","orcid":"https://orcid.org/0000-0001-7558-6198"},"institutions":[{"id":"https://openalex.org/I33585257","display_name":"Anna University, Chennai","ror":"https://ror.org/01qhf1r47","country_code":"IN","type":"education","lineage":["https://openalex.org/I33585257"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"L. Jones Tarcius Doss","raw_affiliation_strings":["Department of Mathematics, Anna University Chennai, CEG Campus, Chennai 600 025, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Anna University Chennai, CEG Campus, Chennai 600 025, India","institution_ids":["https://openalex.org/I33585257"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036537371","display_name":"A. P. Nandini","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. P. Nandini","raw_affiliation_strings":["Department of Mathematics, M.N.M Jain Engineering College, Thoraipakkam, Chennai 600097, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, M.N.M Jain Engineering College, Thoraipakkam, Chennai 600097, India","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5077604862"],"corresponding_institution_ids":["https://openalex.org/I33585257"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07628172,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2012","issue":null,"first_page":"1","last_page":"18"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9958999752998352,"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"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9958999752998352,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9955000281333923,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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":0.8892309665679932},{"id":"https://openalex.org/keywords/petrov\u2013galerkin-method","display_name":"Petrov\u2013Galerkin method","score":0.8534587621688843},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6284134387969971},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6262860298156738},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.557359516620636},{"id":"https://openalex.org/keywords/gauss\u2013kronrod-quadrature-formula","display_name":"Gauss\u2013Kronrod quadrature formula","score":0.5164642333984375},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.510955274105072},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.5094426274299622},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.5084673166275024},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.4881041944026947},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.4672301709651947},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3870301842689514},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.16818958520889282}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8892309665679932},{"id":"https://openalex.org/C2778540877","wikidata":"https://www.wikidata.org/wiki/Q7179155","display_name":"Petrov\u2013Galerkin method","level":3,"score":0.8534587621688843},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6284134387969971},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6262860298156738},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.557359516620636},{"id":"https://openalex.org/C14103991","wikidata":"https://www.wikidata.org/wiki/Q5527852","display_name":"Gauss\u2013Kronrod quadrature formula","level":4,"score":0.5164642333984375},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.510955274105072},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.5094426274299622},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.5084673166275024},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.4881041944026947},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.4672301709651947},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3870301842689514},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.16818958520889282},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2012/962070","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2012/962070","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/962070.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:962070","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2012/962070.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:5e0c8bb4e40f4713a9fe32ebcebcbfbf","is_oa":true,"landing_page_url":"https://doaj.org/article/5e0c8bb4e40f4713a9fe32ebcebcbfbf","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2012 (2012)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/2012/962070","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/962070","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Research Article"}],"best_oa_location":{"id":"doi:10.1155/2012/962070","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2012/962070","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/962070.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1980225330.pdf","grobid_xml":"https://content.openalex.org/works/W1980225330.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W577962163","https://openalex.org/W1565460255","https://openalex.org/W1976573417","https://openalex.org/W1986589023","https://openalex.org/W2019607797","https://openalex.org/W2021670188","https://openalex.org/W2028839436","https://openalex.org/W2047793544","https://openalex.org/W2073732659","https://openalex.org/W2083055483","https://openalex.org/W2092766698","https://openalex.org/W2107777501","https://openalex.org/W2494779131","https://openalex.org/W4250831033"],"related_works":["https://openalex.org/W4387847482","https://openalex.org/W2012929093","https://openalex.org/W4377005030","https://openalex.org/W4205354206","https://openalex.org/W2990351226","https://openalex.org/W3154913590","https://openalex.org/W2337093020","https://openalex.org/W2378736565","https://openalex.org/W2550867510","https://openalex.org/W2764034106"],"abstract_inverted_index":{"A":[0],"quadrature-based":[1],"mixed":[2],"Petrov-Galerkin":[3],"finite":[4],"element":[5],"method":[6],"is":[7],"applied":[8],"to":[9],"a":[10,18,21,27,53],"fourth-order":[11],"linear":[12,29],"ordinary":[13],"differential":[14],"equation.":[15],"After":[16],"employing":[17],"splitting":[19],"technique,":[20],"cubic":[22],"spline":[23],"trial":[24],"space":[25,31],"and":[26],"piecewise":[28],"test":[30],"are":[32,39,57],"considered":[33],"in":[34,47],"the":[35,43,48,63],"method.":[36],"The":[37],"integrals":[38],"then":[40],"replaced":[41],"by":[42],"Gauss":[44],"quadrature":[45],"rule":[46],"formulation":[49],"itself.":[50],"Optimal":[51],"order":[52],"priori":[54],"error":[55],"estimates":[56],"obtained":[58],"without":[59],"any":[60],"restriction":[61],"on":[62],"mesh.":[64]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
