{"id":"https://openalex.org/W2414838631","doi":"https://doi.org/10.1137/16m1065379","title":"Computational Parametric Willmore Flow with Spontaneous Curvature and Area Difference Elasticity Effects","display_name":"Computational Parametric Willmore Flow with Spontaneous Curvature and Area Difference Elasticity Effects","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2414838631","doi":"https://doi.org/10.1137/16m1065379","mag":"2414838631"},"language":"en","primary_location":{"id":"doi:10.1137/16m1065379","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1065379","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/A5071664437","display_name":"John W. Barrett","orcid":"https://orcid.org/0000-0002-4048-1692"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"John W. Barrett","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071758656","display_name":"Harald Garcke","orcid":"https://orcid.org/0000-0001-5235-2073"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Harald Garcke","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5036622790","display_name":"Robert N\u00fcrnberg","orcid":"https://orcid.org/0000-0002-2489-2416"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert N\u00fcrnberg","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071664437"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5289,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.9008884,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"54","issue":"3","first_page":"1732","last_page":"1762"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9961000084877014,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9961000084877014,"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"}},{"id":"https://openalex.org/T11379","display_name":"Rheology and Fluid Dynamics Studies","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/1507","display_name":"Fluid Flow and Transfer Processes"},"field":{"id":"https://openalex.org/fields/15","display_name":"Chemical Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.992900013923645,"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/mathematics","display_name":"Mathematics","score":0.7615485191345215},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.7251105904579163},{"id":"https://openalex.org/keywords/willmore-energy","display_name":"Willmore energy","score":0.6794564723968506},{"id":"https://openalex.org/keywords/elasticity","display_name":"Elasticity (physics)","score":0.6570015549659729},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.6170491576194763},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6119333505630493},{"id":"https://openalex.org/keywords/mean-curvature-flow","display_name":"Mean curvature flow","score":0.5832151770591736},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4571622908115387},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43369758129119873},{"id":"https://openalex.org/keywords/parametric-surface","display_name":"Parametric surface","score":0.4146736264228821},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4131298065185547},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3663262724876404},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32721132040023804},{"id":"https://openalex.org/keywords/mean-curvature","display_name":"Mean curvature","score":0.20981907844543457},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1613364815711975},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07389810681343079}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7615485191345215},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.7251105904579163},{"id":"https://openalex.org/C39428390","wikidata":"https://www.wikidata.org/wiki/Q2581692","display_name":"Willmore energy","level":5,"score":0.6794564723968506},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.6570015549659729},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.6170491576194763},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6119333505630493},{"id":"https://openalex.org/C127813850","wikidata":"https://www.wikidata.org/wiki/Q6803617","display_name":"Mean curvature flow","level":4,"score":0.5832151770591736},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4571622908115387},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43369758129119873},{"id":"https://openalex.org/C2187777","wikidata":"https://www.wikidata.org/wiki/Q1071743","display_name":"Parametric surface","level":3,"score":0.4146736264228821},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4131298065185547},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3663262724876404},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32721132040023804},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.20981907844543457},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1613364815711975},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07389810681343079},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/16m1065379","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1065379","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"},{"id":"pmh:oai:epub.uni-regensburg.de:33130","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401229","display_name":"University of Regensburg Publication Server (University of Regensburg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I60668342","host_organization_name":"University of Regensburg","host_organization_lineage":["https://openalex.org/I60668342"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/report"},{"id":"pmh:oai:epub.uni-regensburg.de:42035","is_oa":false,"landing_page_url":"https://epub.uni-regensburg.de/42035/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401229","display_name":"University of Regensburg Publication Server (University of Regensburg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I60668342","host_organization_name":"University of Regensburg","host_organization_lineage":["https://openalex.org/I60668342"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:iris.unitn.it:11572/283433","is_oa":false,"landing_page_url":"http://hdl.handle.net/11572/283433","pdf_url":null,"source":{"id":"https://openalex.org/S4306401913","display_name":"Institutional Research Information System (Universit\u00e0 degli Studi di Trento)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193223587","host_organization_name":"University of Trento","host_organization_lineage":["https://openalex.org/I193223587"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/30421","is_oa":false,"landing_page_url":"http://hdl.handle.net/10044/1/30421","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"1762","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W7928106","https://openalex.org/W1488071155","https://openalex.org/W1493744162","https://openalex.org/W1504258993","https://openalex.org/W1546875651","https://openalex.org/W1777757636","https://openalex.org/W1840465687","https://openalex.org/W1963537884","https://openalex.org/W1963799857","https://openalex.org/W1979234362","https://openalex.org/W2000545789","https://openalex.org/W2008398287","https://openalex.org/W2014631005","https://openalex.org/W2027016266","https://openalex.org/W2041695053","https://openalex.org/W2049361015","https://openalex.org/W2049876473","https://openalex.org/W2051917325","https://openalex.org/W2058981386","https://openalex.org/W2059162655","https://openalex.org/W2064526255","https://openalex.org/W2064959033","https://openalex.org/W2067257899","https://openalex.org/W2092509712","https://openalex.org/W2112325291","https://openalex.org/W2115218270","https://openalex.org/W2125344654","https://openalex.org/W2145932638","https://openalex.org/W2150388881","https://openalex.org/W2157670588","https://openalex.org/W2159340766","https://openalex.org/W2162463235","https://openalex.org/W2163224702","https://openalex.org/W2340106010","https://openalex.org/W2963618607","https://openalex.org/W3039357072","https://openalex.org/W3104479934"],"related_works":["https://openalex.org/W4317934207","https://openalex.org/W4385277122","https://openalex.org/W2082435022","https://openalex.org/W2737142430","https://openalex.org/W2086072452","https://openalex.org/W4376269649","https://openalex.org/W2034915138","https://openalex.org/W2056627359","https://openalex.org/W2909819188","https://openalex.org/W2000324012"],"abstract_inverted_index":{"A":[0],"new":[1],"stable":[2,85],"continuous-in-time":[3],"semidiscrete":[4],"parametric":[5],"finite":[6],"element":[7],"method":[8,39],"for":[9,17,28,54],"Willmore":[10],"flow":[11],"is":[12],"introduced.":[13],"The":[14,38],"approach":[15],"allows":[16,53],"spontaneous":[18],"curvature":[19],"and":[20,44,72,96],"area":[21,74],"difference":[22],"elasticity":[23],"effects,":[24],"which":[25,61],"are":[26],"important":[27],"many":[29],"applications,":[30],"in":[31,33,81],"particular,":[32,82],"the":[34,45],"context":[35],"of":[36,58,77,87],"membranes.":[37],"extends":[40],"ideas":[41],"from":[42],"Dziuk":[43],"present":[46,97],"authors":[47],"to":[48,64],"obtain":[49,84],"an":[50],"approximation":[51],"that":[52],"a":[55],"tangential":[56],"redistribution":[57],"mesh":[59,66],"points,":[60],"typically":[62],"leads":[63],"better":[65],"properties.":[67],"Moreover,":[68],"we":[69,83],"consider":[70],"volume":[71],"surface":[73],"preserving":[75],"variants":[76,95],"these":[78],"schemes":[79],"and,":[80],"approximations":[86],"Helfrich":[88],"flow.":[89],"We":[90],"also":[91],"discuss":[92],"fully":[93],"discrete":[94],"several":[98],"numerical":[99],"computations.":[100]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
