{"id":"https://openalex.org/W2041207393","doi":"https://doi.org/10.1137/0914065","title":"Multilevel Iteration for Mixed Finite Element Systems with Penalty","display_name":"Multilevel Iteration for Mixed Finite Element Systems with Penalty","publication_year":1993,"publication_date":"1993-09-01","ids":{"openalex":"https://openalex.org/W2041207393","doi":"https://doi.org/10.1137/0914065","mag":"2041207393"},"language":"en","primary_location":{"id":"doi:10.1137/0914065","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0914065","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","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/A5023481731","display_name":"Zhiqiang Cai","orcid":"https://orcid.org/0000-0002-3775-7248"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhiqiang Cai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108364664","display_name":"Charles I. Goldstein","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Charles I. Goldstein","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5113545293","display_name":"Joseph E. Pasciak","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Joseph E. Pasciak","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6352,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.88626609,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"5","first_page":"1072","last_page":"1088"},"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":1.0,"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":1.0,"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":0.9995999932289124,"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":0.9973999857902527,"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":0.757316529750824},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.6826303005218506},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.6819270253181458},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6690154075622559},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6016040444374084},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5432201623916626},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5416039228439331},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.4817114472389221},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4249136447906494},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4050678610801697},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33275705575942993},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.23556232452392578}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.757316529750824},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.6826303005218506},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.6819270253181458},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6690154075622559},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6016040444374084},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5432201623916626},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5416039228439331},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4817114472389221},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4249136447906494},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4050678610801697},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33275705575942993},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.23556232452392578},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0914065","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0914065","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1980158900","https://openalex.org/W2010668310","https://openalex.org/W2018685527","https://openalex.org/W2021921526","https://openalex.org/W2024706945","https://openalex.org/W2026025199","https://openalex.org/W2028357997","https://openalex.org/W2059679865","https://openalex.org/W2064625750","https://openalex.org/W2076582418","https://openalex.org/W2078843646","https://openalex.org/W2095346333","https://openalex.org/W2140803189","https://openalex.org/W2277677093","https://openalex.org/W3147515309","https://openalex.org/W4213380965","https://openalex.org/W4230055019"],"related_works":["https://openalex.org/W2077078424","https://openalex.org/W2182328658","https://openalex.org/W1519938374","https://openalex.org/W84272617","https://openalex.org/W613282331","https://openalex.org/W2092341060","https://openalex.org/W2625595466","https://openalex.org/W2349420447","https://openalex.org/W2058418735","https://openalex.org/W2101742712"],"abstract_inverted_index":{"In":[0],"this":[1,66],"paper,":[2],"the":[3,6,9,24,33,45,56,71,79,90,95],"authors":[4],"consider":[5],"solution":[7,25,46],"of":[8,26,35,47],"discrete":[10],"systems":[11],"that":[12,88],"arises":[13],"when":[14],"a":[15,36,48],"mixed":[16],"finite":[17],"element":[18],"approach":[19,74],"is":[20],"used":[21],"to":[22],"approximate":[23],"second-order":[27],"elliptic":[28],"boundary":[29],"value":[30],"problems.":[31],"By":[32],"introduction":[34],"penalty":[37,53,67],"parameter,":[38],"these":[39],"equations":[40],"can":[41],"be":[42],"approximated":[43],"by":[44,94],"symmetric":[49],"and":[50,63],"positive":[51],"definite":[52],"system":[54,68],"on":[55,70,78],"velocity":[57],"subspace.":[58],"Iterative":[59],"procedures":[60],"are":[61,86],"developed":[62],"analyzed":[64],"for":[65],"based":[69],"hierarchical":[72],"basis":[73],"as":[75,77],"well":[76],"standard":[80],"multigrid":[81],"approach.":[82],"Finally,":[83],"numerical":[84],"experiments":[85],"presented":[87],"illustrate":[89],"convergence":[91],"behavior":[92],"suggested":[93],"theory.":[96]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
