{"id":"https://openalex.org/W3122545788","doi":"https://doi.org/10.1007/s10915-020-01391-x","title":"Asymptotic Behaviour of Time Stepping Methods for Phase Field Models","display_name":"Asymptotic Behaviour of Time Stepping Methods for Phase Field Models","publication_year":2021,"publication_date":"2021-01-16","ids":{"openalex":"https://openalex.org/W3122545788","doi":"https://doi.org/10.1007/s10915-020-01391-x","mag":"3122545788","pmid":"https://pubmed.ncbi.nlm.nih.gov/33505106"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-020-01391-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-020-01391-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-020-01391-x.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","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10915-020-01391-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022915126","display_name":"Xinyu Cheng","orcid":"https://orcid.org/0000-0003-1330-3978"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Xinyu Cheng","raw_affiliation_strings":["Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2 Canada","Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2 Canada","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2, Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100407510","display_name":"Dong Li","orcid":"https://orcid.org/0000-0003-1630-1214"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Dong Li","raw_affiliation_strings":["Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024694851","display_name":"Keith Promislow","orcid":"https://orcid.org/0000-0002-8198-6208"},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Keith Promislow","raw_affiliation_strings":["Department of Mathematics, Michigan State University, East Lansing, 48864 USA","Department of Mathematics, Michigan State University, East Lansing, 48864, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Michigan State University, East Lansing, 48864 USA","institution_ids":["https://openalex.org/I87216513"]},{"raw_affiliation_string":"Department of Mathematics, Michigan State University, East Lansing, 48864, USA","institution_ids":["https://openalex.org/I87216513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091102145","display_name":"Brian Wetton","orcid":"https://orcid.org/0000-0002-6808-6301"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Brian Wetton","raw_affiliation_strings":["Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2 Canada","Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2, Canada"],"raw_orcid":"https://orcid.org/0000-0002-6808-6301","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2 Canada","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2, Canada","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5022915126"],"corresponding_institution_ids":["https://openalex.org/I141945490"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.3203,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.47856718,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"86","issue":"3","first_page":"32","last_page":"32"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9925000071525574,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9692000150680542,"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":0.6654201149940491},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5063904523849487},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4839404225349426},{"id":"https://openalex.org/keywords/metastability","display_name":"Metastability","score":0.48237767815589905},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4554169178009033},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.4547140598297119},{"id":"https://openalex.org/keywords/asymptotically-optimal-algorithm","display_name":"Asymptotically optimal algorithm","score":0.45277056097984314},{"id":"https://openalex.org/keywords/time-stepping","display_name":"Time stepping","score":0.42798566818237305},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4260876774787903},{"id":"https://openalex.org/keywords/fidelity","display_name":"Fidelity","score":0.4259741008281708},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.41852840781211853},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2871595621109009},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2702023983001709},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24113672971725464},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.15243840217590332}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6654201149940491},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5063904523849487},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4839404225349426},{"id":"https://openalex.org/C89464430","wikidata":"https://www.wikidata.org/wiki/Q849516","display_name":"Metastability","level":2,"score":0.48237767815589905},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4554169178009033},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.4547140598297119},{"id":"https://openalex.org/C181789720","wikidata":"https://www.wikidata.org/wiki/Q4812191","display_name":"Asymptotically optimal algorithm","level":2,"score":0.45277056097984314},{"id":"https://openalex.org/C3019693144","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Time stepping","level":3,"score":0.42798566818237305},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4260876774787903},{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.4259741008281708},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.41852840781211853},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2871595621109009},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2702023983001709},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24113672971725464},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.15243840217590332},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10915-020-01391-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-020-01391-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-020-01391-x.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":"pmid:33505106","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33505106","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of scientific computing","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:7811528","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7811528","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"J Sci Comput","raw_type":"Text"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-109861","is_oa":false,"landing_page_url":"http://www.scopus.com/record/display.url?eid=2-s2.0-85100041933&origin=inward","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"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":"Article"},{"id":"pmh:oai:repository.ust.hk:1783.1-109861","is_oa":false,"landing_page_url":"http://repository.ust.hk/ir/Record/1783.1-109861","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s10915-020-01391-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-020-01391-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-020-01391-x.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":[{"display_name":"Affordable and clean energy","score":0.8999999761581421,"id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G8763149811","display_name":null,"funder_award_id":"1813203","funder_id":"https://openalex.org/F4320335353","funder_display_name":"National Science Foundation of Sri Lanka"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320335353","display_name":"National Science Foundation of Sri Lanka","ror":"https://ror.org/010xaa060"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3122545788.pdf","grobid_xml":"https://content.openalex.org/works/W3122545788.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W360456325","https://openalex.org/W1509923322","https://openalex.org/W1971975973","https://openalex.org/W1975968248","https://openalex.org/W1992445851","https://openalex.org/W2025739397","https://openalex.org/W2031651409","https://openalex.org/W2034879619","https://openalex.org/W2041001120","https://openalex.org/W2046528357","https://openalex.org/W2062546043","https://openalex.org/W2068917472","https://openalex.org/W2076143716","https://openalex.org/W2086238793","https://openalex.org/W2128204029","https://openalex.org/W2130698343","https://openalex.org/W2147722083","https://openalex.org/W2169437869","https://openalex.org/W2318086149","https://openalex.org/W2463455424","https://openalex.org/W2501163367","https://openalex.org/W2725599832","https://openalex.org/W2744061310","https://openalex.org/W2766149883","https://openalex.org/W2790325139","https://openalex.org/W2899703448","https://openalex.org/W2911401788","https://openalex.org/W2962738836","https://openalex.org/W2963334563","https://openalex.org/W3005875771","https://openalex.org/W6635892796"],"related_works":["https://openalex.org/W2006961398","https://openalex.org/W2040666836","https://openalex.org/W1990789772","https://openalex.org/W2044869171","https://openalex.org/W2362575449","https://openalex.org/W4232148501","https://openalex.org/W4211229731","https://openalex.org/W2014177369","https://openalex.org/W2078767954","https://openalex.org/W3122545788"],"abstract_inverted_index":{"during":[0],"meta-stable":[1,103],"dynamics.":[2],"The":[3,66,128],"formal":[4,67],"predictions":[5],"are":[6,116,130],"made":[7],"under":[8],"stability":[9],"assumptions":[10],"that":[11,76,96,149],"include":[12],"the":[13,16,20,35,84,106],"preservation":[14],"of":[15,19,38,164],"asymptotic":[17],"structure":[18],"diffuse":[21],"interface,":[22],"a":[23,137],"concept":[24],"we":[25],"call":[26],"profile":[27,110,165],"fidelity.":[28,166],"In":[29],"this":[30],"setting,":[31],"definite":[32],"statements":[33],"about":[34],"relative":[36],"behaviour":[37],"time":[39,62,121,156],"stepping":[40,157],"methods":[41,52,81],"can":[42],"be":[43],"made.":[44],"Some":[45],"methods,":[46,58],"including":[47],"all":[48],"so-called":[49],"energy":[50,79,107],"stable":[51,80],"but":[53],"also":[54],"some":[55,77,89],"fully":[56],"implicit":[57],"require":[59],"asymptotically":[60,132,159],"more":[61,90],"steps":[63,122],"than":[64,88,123],"others.":[65],"analysis":[68,125],"is":[69,100,144],"confirmed":[70],"in":[71,83],"computational":[72],"studies.":[73],"We":[74,93],"observe":[75],"provably":[78],"popular":[82],"literature":[85],"perform":[86],"worse":[87,160],"standard":[91],"schemes.":[92],"show":[94],"further":[95],"when":[97],"Backward":[98],"Euler":[99],"applied":[101],"to":[102,162],"Allen-Cahn":[104],"dynamics,":[105],"decay":[108],"and":[109,147],"fidelity":[111],"properties":[112],"for":[113,118,133,140,150],"these":[114],"discretizations":[115],"preserved":[117],"much":[119],"larger":[120],"previous":[124],"would":[126],"suggest.":[127],"results":[129],"established":[131],"general":[134],"interfaces,":[135],"with":[136],"rigorous":[138],"proof":[139],"radial":[141],"interfaces.":[142],"It":[143],"shown":[145],"analytically":[146],"computationally":[148],"most":[151],"reaction":[152],"terms,":[153],"Eyre":[154],"type":[155],"performs":[158],"due":[161],"loss":[163]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2}],"updated_date":"2026-04-28T14:05:53.105641","created_date":"2025-10-10T00:00:00"}