{"id":"https://openalex.org/W2150353544","doi":"https://doi.org/10.1007/978-3-7091-6282-8_6","title":"Bounds for Eigenvalues with the Use of Finite Elements","display_name":"Bounds for Eigenvalues with the Use of Finite Elements","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2150353544","doi":"https://doi.org/10.1007/978-3-7091-6282-8_6","mag":"2150353544"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-7091-6282-8_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-7091-6282-8_6","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Perspectives on Enclosure Methods","raw_type":"book-chapter"},"type":"book-chapter","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/A5111446766","display_name":"H. C. Heinrich Behnke","orcid":null},"institutions":[{"id":"https://openalex.org/I43980791","display_name":"Clausthal University of Technology","ror":"https://ror.org/04qb8nc58","country_code":"DE","type":"education","lineage":["https://openalex.org/I43980791"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Henning Behnke","raw_affiliation_strings":["TU Clausthal, Institut f\u00fcr Mathematik, Erzstr. 1, D-38678, Clausthal-Zellerfeld, Germany"],"affiliations":[{"raw_affiliation_string":"TU Clausthal, Institut f\u00fcr Mathematik, Erzstr. 1, D-38678, Clausthal-Zellerfeld, Germany","institution_ids":["https://openalex.org/I43980791"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020522818","display_name":"Ulrich Mertins","orcid":null},"institutions":[{"id":"https://openalex.org/I43980791","display_name":"Clausthal University of Technology","ror":"https://ror.org/04qb8nc58","country_code":"DE","type":"education","lineage":["https://openalex.org/I43980791"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ulrich Mertins","raw_affiliation_strings":["TU Clausthal, Institut f\u00fcr Mathematik, Erzstr. 1, D-38678, Clausthal-Zellerfeld, Germany"],"affiliations":[{"raw_affiliation_string":"TU Clausthal, Institut f\u00fcr Mathematik, Erzstr. 1, D-38678, Clausthal-Zellerfeld, Germany","institution_ids":["https://openalex.org/I43980791"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111446766"],"corresponding_institution_ids":["https://openalex.org/I43980791"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.19418639,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"119","last_page":"131"},"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":0.9991999864578247,"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":0.9991999864578247,"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":0.9948999881744385,"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":0.9944999814033508,"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.8588401675224304},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7105231881141663},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5953381657600403},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.573822557926178},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.5298267006874084},{"id":"https://openalex.org/keywords/rayleigh\u2013ritz-method","display_name":"Rayleigh\u2013Ritz method","score":0.5117208957672119},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5101428627967834},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4683356285095215},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.46519505977630615},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32057368755340576},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1377268135547638},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11497044563293457},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.069557785987854},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.062130630016326904}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.8588401675224304},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7105231881141663},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5953381657600403},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.573822557926178},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.5298267006874084},{"id":"https://openalex.org/C70940138","wikidata":"https://www.wikidata.org/wiki/Q852247","display_name":"Rayleigh\u2013Ritz method","level":3,"score":0.5117208957672119},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5101428627967834},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4683356285095215},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.46519505977630615},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32057368755340576},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1377268135547638},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11497044563293457},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.069557785987854},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.062130630016326904},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-7091-6282-8_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-7091-6282-8_6","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Perspectives on Enclosure Methods","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W53809769","https://openalex.org/W79723704","https://openalex.org/W391924885","https://openalex.org/W401415048","https://openalex.org/W1497910784","https://openalex.org/W1522616537","https://openalex.org/W1543114422","https://openalex.org/W1597544196","https://openalex.org/W2025700642","https://openalex.org/W2048795129","https://openalex.org/W2061953601","https://openalex.org/W2064325580","https://openalex.org/W2080151395","https://openalex.org/W2486036103","https://openalex.org/W3022044914"],"related_works":["https://openalex.org/W4220780102","https://openalex.org/W1502401885","https://openalex.org/W2410881844","https://openalex.org/W3196334750","https://openalex.org/W2004257129","https://openalex.org/W2116281088","https://openalex.org/W2016668641","https://openalex.org/W2357551824","https://openalex.org/W2019368960","https://openalex.org/W4686056"],"abstract_inverted_index":null,"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
