{"id":"https://openalex.org/W2905045550","doi":"https://doi.org/10.1137/17m1153285","title":"Finite Element Approximation of Level Set Motion by Powers of the Mean Curvature","display_name":"Finite Element Approximation of Level Set Motion by Powers of the Mean Curvature","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2905045550","doi":"https://doi.org/10.1137/17m1153285","mag":"2905045550"},"language":"en","primary_location":{"id":"doi:10.1137/17m1153285","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1153285","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/A5071446522","display_name":"Axel Kr\u00f6ner","orcid":null},"institutions":[{"id":"https://openalex.org/I4210107641","display_name":"Centre de Math\u00e9matiques Appliqu\u00e9es","ror":"https://ror.org/012e1xn46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210107641","https://openalex.org/I4210141950","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Axel Kr\u00f6ner","raw_affiliation_strings":["CMAP - Centre de Math\u00e9matiques Appliqu\u00e9es de l'Ecole polytechnique (Route de Saclay, 91128 Palaiseau Cedex - France)","Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems (Centre de Math\u00e9matiques Appliqu\u00e9es Ecole Polytechnique Route de Saclay 91128 Palaiseau - France)"],"affiliations":[{"raw_affiliation_string":"CMAP - Centre de Math\u00e9matiques Appliqu\u00e9es de l'Ecole polytechnique (Route de Saclay, 91128 Palaiseau Cedex - France)","institution_ids":["https://openalex.org/I4210107641","https://openalex.org/I142476485"]},{"raw_affiliation_string":"Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems (Centre de Math\u00e9matiques Appliqu\u00e9es Ecole Polytechnique Route de Saclay 91128 Palaiseau - France)","institution_ids":["https://openalex.org/I4210107641","https://openalex.org/I142476485"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007066824","display_name":"Eva Kr\u00f6ner","orcid":null},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Eva Kr\u00f6ner","raw_affiliation_strings":["Georg-August-University = Georg-August-Universit\u00e4t G\u00f6ttingen (Wilhelmsplatz 1, 37073 G\u00f6ttingen, Allemagne - Germany)"],"affiliations":[{"raw_affiliation_string":"Georg-August-University = Georg-August-Universit\u00e4t G\u00f6ttingen (Wilhelmsplatz 1, 37073 G\u00f6ttingen, Allemagne - Germany)","institution_ids":["https://openalex.org/I74656192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004489825","display_name":"Heiko Kr\u00f6ner","orcid":null},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Heiko Kr\u00f6ner","raw_affiliation_strings":["Department of Mathematics - University of Hamburg (Bundesstra\u00dfe 55 D-20146 Hamburg - Germany)"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics - University of Hamburg (Bundesstra\u00dfe 55 D-20146 Hamburg - Germany)","institution_ids":["https://openalex.org/I159176309"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071446522"],"corresponding_institution_ids":["https://openalex.org/I142476485","https://openalex.org/I4210107641"],"apc_list":null,"apc_paid":null,"fwci":0.8107,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.71157861,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"40","issue":"6","first_page":"A4158","last_page":"A4183"},"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":0.9973000288009644,"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":0.9973000288009644,"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":0.9948999881744385,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9925000071525574,"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":0.8126667737960815},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6861402988433838},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.6366147994995117},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6116644740104675},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.565900444984436},{"id":"https://openalex.org/keywords/mean-curvature-flow","display_name":"Mean curvature flow","score":0.5019316673278809},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.48735910654067993},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45576462149620056},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4278680086135864},{"id":"https://openalex.org/keywords/mean-curvature","display_name":"Mean curvature","score":0.270069420337677},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17199507355690002}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8126667737960815},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6861402988433838},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.6366147994995117},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6116644740104675},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.565900444984436},{"id":"https://openalex.org/C127813850","wikidata":"https://www.wikidata.org/wiki/Q6803617","display_name":"Mean curvature flow","level":4,"score":0.5019316673278809},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.48735910654067993},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45576462149620056},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4278680086135864},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.270069420337677},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17199507355690002},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/17m1153285","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1153285","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":61,"referenced_works":["https://openalex.org/W623652321","https://openalex.org/W1447382235","https://openalex.org/W1491650242","https://openalex.org/W1492326914","https://openalex.org/W1498500832","https://openalex.org/W1553761880","https://openalex.org/W1558133826","https://openalex.org/W1580269359","https://openalex.org/W1830094849","https://openalex.org/W1965110070","https://openalex.org/W1973369053","https://openalex.org/W1978539725","https://openalex.org/W1981280745","https://openalex.org/W1991113069","https://openalex.org/W1999545889","https://openalex.org/W2008398287","https://openalex.org/W2008795550","https://openalex.org/W2009166934","https://openalex.org/W2009429030","https://openalex.org/W2014932286","https://openalex.org/W2018251972","https://openalex.org/W2018573482","https://openalex.org/W2018686874","https://openalex.org/W2023111506","https://openalex.org/W2032316144","https://openalex.org/W2033021023","https://openalex.org/W2036670771","https://openalex.org/W2040805941","https://openalex.org/W2043304250","https://openalex.org/W2049361015","https://openalex.org/W2050059859","https://openalex.org/W2050816808","https://openalex.org/W2054967428","https://openalex.org/W2055603467","https://openalex.org/W2056087726","https://openalex.org/W2056992872","https://openalex.org/W2058981386","https://openalex.org/W2065164181","https://openalex.org/W2081820511","https://openalex.org/W2082052570","https://openalex.org/W2082187902","https://openalex.org/W2093834886","https://openalex.org/W2095464771","https://openalex.org/W2102635728","https://openalex.org/W2109973988","https://openalex.org/W2111024532","https://openalex.org/W2112311198","https://openalex.org/W2115218270","https://openalex.org/W2122833107","https://openalex.org/W2144133758","https://openalex.org/W2479659699","https://openalex.org/W2556144662","https://openalex.org/W2599473381","https://openalex.org/W2611525126","https://openalex.org/W2767697585","https://openalex.org/W2963017886","https://openalex.org/W2963116825","https://openalex.org/W2963730941","https://openalex.org/W2976551932","https://openalex.org/W3022122637","https://openalex.org/W4249276713"],"related_works":["https://openalex.org/W2353039109","https://openalex.org/W2900100504","https://openalex.org/W4315588385","https://openalex.org/W3124638673","https://openalex.org/W4245687327","https://openalex.org/W2066153363","https://openalex.org/W2061564118","https://openalex.org/W2112549839","https://openalex.org/W4318566977","https://openalex.org/W2897268649"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2,203],"we":[3,21,115,162,176,204],"study":[4,108],"the":[5,23,31,36,43,63,71,74,89,109,120,125,132,138,142,158,164,169,173,180,199,202,208],"level":[6,47,182],"set":[7,48,183],"formulations":[8],"of":[9,18,30,73,88,113,124,160,201],"certain":[10],"geometric":[11],"evolution":[12],"equations":[13,45,68,78,127],"from":[14],"a":[15,57,153,193],"numerical":[16,135],"point":[17],"view.":[19],"Specifically,":[20],"consider":[22],"flow":[24,40],"by":[25,96],"powers":[26],"greater":[27],"than":[28],"one":[29],"mean":[32,38],"curvature":[33,39],"(PMCF)":[34],"and":[35,53,85,99,188],"inverse":[37],"(IMCF).":[41],"Since":[42],"corresponding":[44],"in":[46,62,86,141,152,157,192,207],"form":[49],"are":[50],"quasi-linear,":[51],"degenerate,":[52],"especially":[54],"possibly":[55],"singular":[56],"regularization":[58,83,139,174],"method":[59],"is":[60,149],"used":[61],"literature":[64],"to":[65,69,171],"approximate":[66],"these":[67],"overcome":[70],"singularities":[72],"equations.":[75],"The":[76],"regularized":[77,126,181],"depend":[79],"both":[80,147],"on":[81,92],"an":[82],"parameter":[84],"case":[87,145,159],"ICMF":[90],"additionally":[91],"further":[93,191],"parameters.":[94,166],"Motivated":[95],"Feng,":[97],"Neilan,":[98],"Prohl":[100],"[Numer.":[101],"Math.,":[102],"108":[103],"(2007),":[104],"pp.":[105],"93--119],":[106],"who":[107],"finite":[110,121],"element":[111,122],"approximation":[112,123],"IMCF,":[114],"prove":[116],"error":[117,140,175],"estimates":[118],"for":[119,128,146,179],"PMCF.":[129],"We":[130],"validate":[131],"rates":[133],"with":[134],"examples.":[136],"Additionally,":[137],"rotationally":[143,194],"symmetric":[144,195],"flows":[148],"numerically":[150],"analyzed":[151],"two-dimensional":[154],"setting.":[155],"Therefore,":[156],"IMCF":[161,184],"fix":[163],"additional":[165],"Furthermore,":[167],"having":[168],"goal":[170],"estimate":[172],"derive":[177],"barriers":[178],"respecting":[185],"all":[186],"parameters":[187],"specify":[189],"them":[190],"simplified":[196],"case.":[197,210],"At":[198],"end":[200],"present":[205],"simulations":[206],"three-dimensional":[209]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
