{"id":"https://openalex.org/W1980342674","doi":"https://doi.org/10.1137/s0036142998337697","title":"Numerical Analysis of Compatible Phase Transitions in Elastic Solids","display_name":"Numerical Analysis of Compatible Phase Transitions in Elastic Solids","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1980342674","doi":"https://doi.org/10.1137/s0036142998337697","mag":"1980342674"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142998337697","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142998337697","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5036808184","display_name":"Carsten Carstensen","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Carsten Carstensen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5014213782","display_name":"Petr Plech\u00e1\u010d","orcid":"https://orcid.org/0000-0003-2102-4485"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Petr Plech\u00e1c","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036808184"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.3107,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.93758612,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"37","issue":"6","first_page":"2061","last_page":"2081"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T11366","display_name":"Elasticity and Material Modeling","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T11558","display_name":"Composite Material Mechanics","score":0.9991000294685364,"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":0.998199999332428,"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":0.7179845571517944},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7034633159637451},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6845223307609558},{"id":"https://openalex.org/keywords/elasticity","display_name":"Elasticity (physics)","score":0.6087514758110046},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5967578887939453},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5744094848632812},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5491764545440674},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5046929121017456},{"id":"https://openalex.org/keywords/phase-field-models","display_name":"Phase field models","score":0.48672178387641907},{"id":"https://openalex.org/keywords/stress-field","display_name":"Stress field","score":0.4527462124824524},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3902897536754608},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.3633285164833069},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2962087392807007},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20112022757530212}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7179845571517944},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7034633159637451},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6845223307609558},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.6087514758110046},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5967578887939453},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5744094848632812},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5491764545440674},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5046929121017456},{"id":"https://openalex.org/C2780568864","wikidata":"https://www.wikidata.org/wiki/Q1640482","display_name":"Phase field models","level":3,"score":0.48672178387641907},{"id":"https://openalex.org/C2778414698","wikidata":"https://www.wikidata.org/wiki/Q7623438","display_name":"Stress field","level":3,"score":0.4527462124824524},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3902897536754608},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.3633285164833069},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2962087392807007},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20112022757530212},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142998337697","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142998337697","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.800000011920929,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W160043448","https://openalex.org/W1014243776","https://openalex.org/W1492326914","https://openalex.org/W1498113553","https://openalex.org/W1512048500","https://openalex.org/W1537639429","https://openalex.org/W1977950843","https://openalex.org/W2003787597","https://openalex.org/W2004765086","https://openalex.org/W2010645022","https://openalex.org/W2027582252","https://openalex.org/W2030579135","https://openalex.org/W2033761099","https://openalex.org/W2045970486","https://openalex.org/W2054535420","https://openalex.org/W2065000345","https://openalex.org/W2070108649","https://openalex.org/W2071036364","https://openalex.org/W2072092546","https://openalex.org/W2076074132","https://openalex.org/W2078012222","https://openalex.org/W2084277536","https://openalex.org/W2135537438","https://openalex.org/W2148639620","https://openalex.org/W2158291708","https://openalex.org/W2274629352","https://openalex.org/W2327623587","https://openalex.org/W4285719527","https://openalex.org/W4292166829"],"related_works":["https://openalex.org/W2529287984","https://openalex.org/W2058166223","https://openalex.org/W2146284271","https://openalex.org/W2412659219","https://openalex.org/W3005696751","https://openalex.org/W159684413","https://openalex.org/W2341496509","https://openalex.org/W1985770928","https://openalex.org/W2258510569","https://openalex.org/W2032531991"],"abstract_inverted_index":{"The":[0],"variational":[1],"model":[2],"of":[3,31,42,64,99,123],"phase":[4],"transitions":[5],"for":[6,94],"elastic":[7],"materials":[8,125],"based":[9,106],"on":[10],"linearized":[11],"elasticity":[12],"leads":[13],"to":[14,72],"a":[15,22,57,78,83,85,88],"nonconvex":[16],"minimization":[17],"problem":[18,59],"(P)":[19],"in":[20,38,56,69],"which":[21],"minimum":[23],"need":[24],"not":[25],"be":[26],"attained.":[27],"In":[28],"the":[29,34,48,52,65,95,100,104,120,124],"design":[30],"advanced":[32],"materials,":[33],"main":[35],"interest":[36],"is":[37,92,109],"reliable":[39],"numerical":[40,80],"predictions":[41],"certain":[43],"macroscopic":[44,121],"quantities":[45],"such":[46],"as":[47],"global":[49],"deformation":[50],"and":[51,87],"stress":[53,101],"field":[54],"determined":[55],"relaxed":[58],"(QP).":[60],"An":[61],"explicit":[62],"formula":[63],"quasi-convexified":[66],"energy":[67],"density":[68],"(QP)":[70],"due":[71],"R.V.":[73],"Kohn":[74],"provides":[75],"us":[76],"with":[77,129],"well-posed":[79],"problem.":[81],"First,":[82],"mathematical":[84],"priori":[86],"posteriori":[89],"error":[90,107,131],"analysis":[91],"established":[93],"finite":[96],"element":[97],"approximation":[98],"variable;":[102],"then":[103],"residual":[105],"indicator":[108],"implemented":[110],"within":[111],"an":[112],"adaptive":[113],"mesh-refinement":[114],"algorithm.":[115],"Numerical":[116],"examples":[117],"illustrate":[118],"that":[119],"properties":[122],"are":[126],"computed":[127],"efficiently":[128],"appropriate":[130],"control.":[132]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-02-25T08:12:03.925757","created_date":"2025-10-10T00:00:00"}