{"id":"https://openalex.org/W2772555808","doi":"https://doi.org/10.1137/17m1159166","title":"Unconditional Stability of Semi-Implicit Discretizations of Singular Flows","display_name":"Unconditional Stability of Semi-Implicit Discretizations of Singular Flows","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2772555808","doi":"https://doi.org/10.1137/17m1159166","mag":"2772555808"},"language":"en","primary_location":{"id":"doi:10.1137/17m1159166","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1159166","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1712.03260","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017359935","display_name":"S\u00f6ren Bartels","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"S\u00f6ren Bartels","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010484841","display_name":"Lars Diening","orcid":"https://orcid.org/0000-0002-0523-3079"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lars Diening","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5040883953","display_name":"Ricardo H. Nochetto","orcid":"https://orcid.org/0009-0002-8895-1144"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ricardo H. Nochetto","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5017359935"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00638795,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"56","issue":"3","first_page":"1896","last_page":"1914"},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9994000196456909,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.7452390789985657},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.739570677280426},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6837602853775024},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6165634393692017},{"id":"https://openalex.org/keywords/discretization-error","display_name":"Discretization error","score":0.5318951606750488},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.5009887218475342},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4940502941608429},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4816914498806},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.47661152482032776},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4525831937789917},{"id":"https://openalex.org/keywords/time-stepping","display_name":"Time stepping","score":0.42036116123199463},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36633822321891785},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16371279954910278},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10720959305763245}],"concepts":[{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.7452390789985657},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.739570677280426},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6837602853775024},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6165634393692017},{"id":"https://openalex.org/C126148662","wikidata":"https://www.wikidata.org/wiki/Q3890355","display_name":"Discretization error","level":3,"score":0.5318951606750488},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.5009887218475342},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4940502941608429},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4816914498806},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.47661152482032776},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4525831937789917},{"id":"https://openalex.org/C3019693144","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Time stepping","level":3,"score":0.42036116123199463},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36633822321891785},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16371279954910278},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10720959305763245},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/17m1159166","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1159166","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:arXiv.org:1712.03260","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.03260","pdf_url":"https://arxiv.org/pdf/1712.03260","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"mag:2772555808","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1712.03260.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:pub.uni-bielefeld.de:2921250","is_oa":false,"landing_page_url":"https://pub.uni-bielefeld.de/record/2921250","pdf_url":null,"source":{"id":"https://openalex.org/S4306401624","display_name":"Publikationen an der Universit\u00e4t Bielefeld (Universit\u00e4t Bielefeld)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20121455","host_organization_name":"Bielefeld University","host_organization_lineage":["https://openalex.org/I20121455"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Bartels S, Diening L, Nochetto RH. UNCONDITIONAL STABILITY OF SEMI-IMPLICIT DISCRETIZATIONS OF SINGULAR FLOWS. <em>SIAM JOURNAL ON NUMERICAL ANALYSIS</em>. 2018;56(3):1896-1914.","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pub.uni-bielefeld.de:2934679","is_oa":false,"landing_page_url":"https://pub.uni-bielefeld.de/record/2934679","pdf_url":null,"source":{"id":"https://openalex.org/S4306401624","display_name":"Publikationen an der Universit\u00e4t Bielefeld (Universit\u00e4t Bielefeld)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20121455","host_organization_name":"Bielefeld University","host_organization_lineage":["https://openalex.org/I20121455"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Bartels S, Diening L, Nochetto RH. Unconditional Stability of Semi-Implicit Discretizations of Singular Flows. <em>SIAM Journal on Numerical Analysis</em>. 2018;56(3):1896-1914.","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1712.03260","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1712.03260","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1712.03260","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.03260","pdf_url":"https://arxiv.org/pdf/1712.03260","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[{"score":0.75,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G1681180284","display_name":null,"funder_award_id":"DMS-1411808","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G188083318","display_name":null,"funder_award_id":"SPP-1962","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G4816005617","display_name":null,"funder_award_id":"1411808","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320337180","display_name":"Hausdorff Research Institute for Mathematics","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2772555808.pdf","grobid_xml":"https://content.openalex.org/works/W2772555808.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W418503264","https://openalex.org/W1582617215","https://openalex.org/W1970610330","https://openalex.org/W1970734370","https://openalex.org/W1980939071","https://openalex.org/W1988307074","https://openalex.org/W2012423916","https://openalex.org/W2043267610","https://openalex.org/W2053188289","https://openalex.org/W2053951212","https://openalex.org/W2065383341","https://openalex.org/W2068432368","https://openalex.org/W2086739819","https://openalex.org/W2089231054","https://openalex.org/W2089586835","https://openalex.org/W2089773056","https://openalex.org/W2115218270","https://openalex.org/W2416750559"],"related_works":["https://openalex.org/W2066145581","https://openalex.org/W2950523975","https://openalex.org/W1978346204","https://openalex.org/W1968510453","https://openalex.org/W2963535445","https://openalex.org/W2345026483","https://openalex.org/W2900329199","https://openalex.org/W2558783215","https://openalex.org/W33758314","https://openalex.org/W2963914755","https://openalex.org/W2885919413","https://openalex.org/W2793119921","https://openalex.org/W2609086070","https://openalex.org/W2885092532","https://openalex.org/W3201213858","https://openalex.org/W2768306041","https://openalex.org/W2068432368","https://openalex.org/W2042116764","https://openalex.org/W2762430962","https://openalex.org/W2963236482"],"abstract_inverted_index":{"A":[0],"popular":[1],"and":[2,29,75],"efficient":[3],"discretization":[4],"of":[5,17],"evolutions":[6],"involving":[7],"the":[8,18],"singular":[9,32],"$p$-Laplace":[10],"operator":[11,20],"is":[12,26,35,39],"based":[13],"on":[14,59],"a":[15,22,30,60],"factorization":[16],"differential":[19],"into":[21],"linear":[23],"part":[24],"which":[25,34],"treated":[27,36],"implicitly":[28],"regularized":[31],"factor":[33],"explicitly.":[37],"It":[38],"shown":[40],"that":[41,78],"an":[42],"unconditional":[43],"energy":[44],"stability":[45],"property":[46],"for":[47,71],"this":[48,79],"semi-implicit":[49],"time":[50],"stepping":[51],"strategy":[52],"holds.":[53],"Related":[54],"error":[55],"estimates":[56],"depend":[57],"critically":[58],"required":[61],"regularization":[62,73],"parameter.":[63],"Numerical":[64],"experiments":[65],"reveal":[66],"reduced":[67],"experimental":[68],"convergence":[69],"rates":[70],"smaller":[72],"parameters":[74],"thereby":[76],"confirm":[77],"dependence":[80],"cannot":[81],"be":[82],"avoided":[83],"in":[84],"general.":[85]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}