{"id":"https://openalex.org/W2021574056","doi":"https://doi.org/10.2478/cmam-2010-0008","title":"Analysis of a Class of Penalty Methods for Computing Singular Minimizers","display_name":"Analysis of a Class of Penalty Methods for Computing Singular Minimizers","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2021574056","doi":"https://doi.org/10.2478/cmam-2010-0008","mag":"2021574056"},"language":"en","primary_location":{"id":"doi:10.2478/cmam-2010-0008","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2010-0008","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2010-0008/pdf","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","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":true,"oa_status":"hybrid","oa_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2010-0008/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036808184","display_name":"Carsten Carstensen","orcid":null},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"C. Carstensen","raw_affiliation_strings":["1Humboldt-Universit\u00a8at zu Berlin, Unter den Linden 6, 10099 Berlin, Germany","University of Oxford"],"affiliations":[{"raw_affiliation_string":"1Humboldt-Universit\u00a8at zu Berlin, Unter den Linden 6, 10099 Berlin, Germany","institution_ids":[]},{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061841111","display_name":"Christoph Ortner","orcid":"https://orcid.org/0000-0003-1498-8120"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C. Ortner","raw_affiliation_strings":["2Mathematical Institute, University of Oxford, 24-29 St Giles\u2019, Oxford OX1 3LB, UK"],"affiliations":[{"raw_affiliation_string":"2Mathematical Institute, University of Oxford, 24-29 St Giles\u2019, Oxford OX1 3LB, UK","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036808184"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":0.6864,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.7204176,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"10","issue":"2","first_page":"137","last_page":"163"},"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":0.9988999962806702,"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":0.9988999962806702,"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":0.9954000115394592,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9954000115394592,"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/discretization","display_name":"Discretization","score":0.7381816506385803},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.675805926322937},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.6707407236099243},{"id":"https://openalex.org/keywords/phenomenon","display_name":"Phenomenon","score":0.6072947978973389},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5799034833908081},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5702077150344849},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5276281237602234},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5087197422981262},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5014665126800537},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.49113866686820984},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4360211193561554},{"id":"https://openalex.org/keywords/calculus-of-variations","display_name":"Calculus of variations","score":0.4303617477416992},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4246181845664978},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3723592162132263},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36978214979171753},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3359541893005371},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10645970702171326}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7381816506385803},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.675805926322937},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.6707407236099243},{"id":"https://openalex.org/C50335755","wikidata":"https://www.wikidata.org/wiki/Q483247","display_name":"Phenomenon","level":2,"score":0.6072947978973389},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5799034833908081},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5702077150344849},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5276281237602234},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5087197422981262},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5014665126800537},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.49113866686820984},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4360211193561554},{"id":"https://openalex.org/C97985569","wikidata":"https://www.wikidata.org/wiki/Q216861","display_name":"Calculus of variations","level":2,"score":0.4303617477416992},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4246181845664978},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3723592162132263},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36978214979171753},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3359541893005371},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10645970702171326},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2478/cmam-2010-0008","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2010-0008","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2010-0008/pdf","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:wrap.warwick.ac.uk:43755","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.670.5423","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.670.5423","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://homepages.warwick.ac.uk/staff/C.Ortner/pdfs/2010-CMAM-PenaltyMethod.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.2478/cmam-2010-0008","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2010-0008","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2010-0008/pdf","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.6200000047683716}],"awards":[{"id":"https://openalex.org/G1601545921","display_name":null,"funder_award_id":"R31-2008-000-10049-0","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G2690613784","display_name":null,"funder_award_id":"R31-2008-000-10049-0","funder_id":"https://openalex.org/F4320322349","funder_display_name":"Ministry of Education, Science and Technology"},{"id":"https://openalex.org/G4115941747","display_name":null,"funder_award_id":"Ministry of Education","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8828949111","display_name":null,"funder_award_id":"Forschergruppe 797","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320322349","display_name":"Ministry of Education, Science and Technology","ror":"https://ror.org/01p262204"},{"id":"https://openalex.org/F4320328568","display_name":"Hausdorff Center for Mathematics","ror":null},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2021574056.pdf","grobid_xml":"https://content.openalex.org/works/W2021574056.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W649818166","https://openalex.org/W656727543","https://openalex.org/W1492326914","https://openalex.org/W1537639429","https://openalex.org/W1591473593","https://openalex.org/W1593038947","https://openalex.org/W1979382551","https://openalex.org/W1989623088","https://openalex.org/W2008197760","https://openalex.org/W2010716184","https://openalex.org/W2015371032","https://openalex.org/W2017618723","https://openalex.org/W2020327980","https://openalex.org/W2048853822","https://openalex.org/W2088703872","https://openalex.org/W2103652837","https://openalex.org/W2116886664","https://openalex.org/W2123354485","https://openalex.org/W2132207368","https://openalex.org/W2305185103","https://openalex.org/W2328723724","https://openalex.org/W2487440882","https://openalex.org/W3023103952","https://openalex.org/W3204708751","https://openalex.org/W4294678829","https://openalex.org/W6602071156"],"related_works":["https://openalex.org/W4300450609","https://openalex.org/W4386931570","https://openalex.org/W2391010541","https://openalex.org/W2006251942","https://openalex.org/W2357367123","https://openalex.org/W4388930439","https://openalex.org/W2364741597","https://openalex.org/W2387276901","https://openalex.org/W1492103595","https://openalex.org/W2057218235"],"abstract_inverted_index":{"Abstract":[0],"Amongst":[1],"the":[2,7,15,21,38,53,56,60,77,80,98,108,111,116,119],"more":[3],"exciting":[4],"phenomena":[5],"in":[6,20,59,76],"field":[8],"of":[9,23,55,63,79,110,118],"nonlinear":[10],"partial":[11],"differential":[12],"equations":[13],"is":[14,41],"Lavrentiev":[16,39,57,81],"phenomenon":[17,40,58,82],"which":[18],"occurs":[19],"calculus":[22,62],"variations.":[24,64],"We":[25,65,90],"prove":[26],"that":[27],"a":[28,69,85],"conforming":[29],"finite":[30,45],"element":[31,46],"method":[32],"fails":[33],"if":[34,37],"and":[35,67,87,114],"only":[36],"present.":[42],"Consequently,":[43],"nonstandard":[44],"methods":[47],"have":[48],"to":[49],"be":[50],"designed":[51],"for":[52,72,107,115],"detection":[54],"computational":[61],"formulate":[66],"analyze":[68],"general":[70],"strategy":[71],"solving":[73],"variational":[74],"problems":[75,113],"presence":[78],"based":[83],"on":[84,97],"splitting":[86],"penalization":[88],"strategy.":[89],"establish":[91],"convergence":[92],"results":[93],"under":[94],"mild":[95],"conditions":[96],"stored":[99],"energy":[100],"function.":[101],"Moreover,":[102],"we":[103],"present":[104],"practical":[105],"strategies":[106],"solution":[109],"discretized":[112],"choice":[117],"penalty":[120],"parameter.":[121]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}