{"id":"https://openalex.org/W4395003325","doi":"https://doi.org/10.1007/s10915-024-02530-4","title":"An Implicitly Extended Crank\u2013Nicolson Scheme for the Heat Equation on a Time-Dependent Domain","display_name":"An Implicitly Extended Crank\u2013Nicolson Scheme for the Heat Equation on a Time-Dependent Domain","publication_year":2024,"publication_date":"2024-04-22","ids":{"openalex":"https://openalex.org/W4395003325","doi":"https://doi.org/10.1007/s10915-024-02530-4"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-024-02530-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-024-02530-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-024-02530-4.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10915-024-02530-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089012830","display_name":"Stefan Frei","orcid":"https://orcid.org/0000-0002-4507-4690"},"institutions":[{"id":"https://openalex.org/I189712700","display_name":"University of Konstanz","ror":"https://ror.org/0546hnb39","country_code":"DE","type":"education","lineage":["https://openalex.org/I189712700"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Stefan Frei","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Konstanz, 78457, Konstanz, Germany"],"raw_orcid":"https://orcid.org/0000-0002-4507-4690","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Konstanz, 78457, Konstanz, Germany","institution_ids":["https://openalex.org/I189712700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016163083","display_name":"Maneesh Kumar Singh","orcid":"https://orcid.org/0000-0003-2623-5441"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Maneesh Kumar Singh","raw_affiliation_strings":["Department of Mathematics, Imperial College London, London, SW7 2AZ, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Imperial College London, London, SW7 2AZ, UK","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089012830"],"corresponding_institution_ids":["https://openalex.org/I189712700"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.9636,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.83405037,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"99","issue":"3","first_page":null,"last_page":null},"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":0.9990000128746033,"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":0.9990000128746033,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9983999729156494,"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/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/crank\u2013nicolson-method","display_name":"Crank\u2013Nicolson method","score":0.897127628326416},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.89451003074646},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.6996920108795166},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5978860259056091},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5836377143859863},{"id":"https://openalex.org/keywords/crank","display_name":"Crank","score":0.5511698722839355},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46633434295654297},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3528149724006653},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1319318413734436}],"concepts":[{"id":"https://openalex.org/C180931078","wikidata":"https://www.wikidata.org/wiki/Q588725","display_name":"Crank\u2013Nicolson method","level":3,"score":0.897127628326416},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.89451003074646},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.6996920108795166},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5978860259056091},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5836377143859863},{"id":"https://openalex.org/C198994188","wikidata":"https://www.wikidata.org/wiki/Q857558","display_name":"Crank","level":3,"score":0.5511698722839355},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46633434295654297},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3528149724006653},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1319318413734436},{"id":"https://openalex.org/C203311528","wikidata":"https://www.wikidata.org/wiki/Q34132","display_name":"Cylinder","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10915-024-02530-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-024-02530-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-024-02530-4.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:kops.uni-konstanz.de:123456789/69972","is_oa":true,"landing_page_url":"http://nbn-resolving.de/urn:nbn:de:bsz:352-2-1i4kfd9m65oqf1","pdf_url":null,"source":{"id":"https://openalex.org/S4306401487","display_name":"KOPS (University of Konstanz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I189712700","host_organization_name":"University of Konstanz","host_organization_lineage":["https://openalex.org/I189712700"],"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":"Journal of Scientific Computing. Springer. 2024, 99(3), 64. ISSN 0885-7474. eISSN 1573-7691. Verf\u00fcgbar unter: doi: 10.1007/s10915-024-02530-4","raw_type":"doc-type:Text"}],"best_oa_location":{"id":"doi:10.1007/s10915-024-02530-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-024-02530-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-024-02530-4.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320326505","display_name":"Universit\u00e4t Konstanz","ror":"https://ror.org/0546hnb39"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4395003325.pdf"},"referenced_works_count":60,"referenced_works":["https://openalex.org/W55168570","https://openalex.org/W311630916","https://openalex.org/W1572985915","https://openalex.org/W1984426476","https://openalex.org/W1986005695","https://openalex.org/W1994323853","https://openalex.org/W1997235068","https://openalex.org/W2000194797","https://openalex.org/W2007072559","https://openalex.org/W2015058476","https://openalex.org/W2015418516","https://openalex.org/W2017605853","https://openalex.org/W2027006272","https://openalex.org/W2031407958","https://openalex.org/W2040896717","https://openalex.org/W2055794370","https://openalex.org/W2062560968","https://openalex.org/W2065234719","https://openalex.org/W2079423956","https://openalex.org/W2082621526","https://openalex.org/W2092922615","https://openalex.org/W2098258814","https://openalex.org/W2104152474","https://openalex.org/W2108460616","https://openalex.org/W2114241072","https://openalex.org/W2117496726","https://openalex.org/W2133686935","https://openalex.org/W2146926056","https://openalex.org/W2154602877","https://openalex.org/W2163914949","https://openalex.org/W2176375880","https://openalex.org/W2212370034","https://openalex.org/W2246232185","https://openalex.org/W2266052957","https://openalex.org/W2554940741","https://openalex.org/W2579019105","https://openalex.org/W2581758183","https://openalex.org/W2583875019","https://openalex.org/W2610388470","https://openalex.org/W2737794616","https://openalex.org/W2747023022","https://openalex.org/W2809782784","https://openalex.org/W2886188545","https://openalex.org/W2962869991","https://openalex.org/W2963825807","https://openalex.org/W2963890183","https://openalex.org/W2974473399","https://openalex.org/W2979712688","https://openalex.org/W2981039664","https://openalex.org/W2990502025","https://openalex.org/W3005399188","https://openalex.org/W3101182803","https://openalex.org/W3138749827","https://openalex.org/W3162463646","https://openalex.org/W3204708751","https://openalex.org/W3217186294","https://openalex.org/W4236797139","https://openalex.org/W4236938392","https://openalex.org/W4323275669","https://openalex.org/W6697676117"],"related_works":["https://openalex.org/W142251042","https://openalex.org/W1968062609","https://openalex.org/W2392419558","https://openalex.org/W2362797524","https://openalex.org/W3159050253","https://openalex.org/W2376230854","https://openalex.org/W2184193744","https://openalex.org/W2068795416","https://openalex.org/W3010321090","https://openalex.org/W2045374466"],"abstract_inverted_index":{"Abstract":[0],"We":[1,69],"consider":[2],"a":[3,14,62,71,73,90],"time-stepping":[4],"scheme":[5],"of":[6,31],"Crank\u2013Nicolson":[7],"type":[8],"for":[9,111],"the":[10,21,32,35,107],"heat":[11],"equation":[12],"on":[13,55],"moving":[15],"domain":[16,23],"in":[17,77,83,87,99],"Eulerian":[18],"coordinates.":[19],"As":[20],"spatial":[22,60],"varies":[24],"between":[25],"subsequent":[26],"time":[27,37,88,114],"steps,":[28],"an":[29,51],"extension":[30,53],"solution":[33],"from":[34],"previous":[36],"step":[38],"is":[39,67],"required.":[40],"Following":[41],"Lehrenfeld":[42],"and":[43,79,101],"Olskanskii":[44],"(ESAIM:":[45],"M2AN":[46],"53(2):585\u2013614,":[47],"2019),":[48],"we":[49,95],"apply":[50],"implicit":[52],"based":[54],"so-called":[56],"ghost-penalty":[57],"terms.":[58],"For":[59],"discretisation,":[61],"cut":[63],"finite":[64],"element":[65],"method":[66],"used.":[68],"derive":[70],"complete":[72],"priori":[74],"error":[75],"analysis":[76],"space":[78,103],"time,":[80],"which":[81],"shows":[82],"particular":[84],"second-order":[85],"convergence":[86],"under":[89],"parabolic":[91],"CFL":[92],"condition.":[93],"Finally,":[94],"present":[96],"numerical":[97],"results":[98],"two":[100],"three":[102],"dimensions":[104],"that":[105],"confirm":[106],"analytical":[108],"estimates,":[109],"even":[110],"much":[112],"larger":[113],"steps.":[115]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}
