{"id":"https://openalex.org/W4294653772","doi":"https://doi.org/10.1007/s00332-022-09844-3","title":"An Explicit Adaptive Finite Difference Method for the Cahn\u2013Hilliard Equation","display_name":"An Explicit Adaptive Finite Difference Method for the Cahn\u2013Hilliard Equation","publication_year":2022,"publication_date":"2022-09-05","ids":{"openalex":"https://openalex.org/W4294653772","doi":"https://doi.org/10.1007/s00332-022-09844-3","pmid":"https://pubmed.ncbi.nlm.nih.gov/36089998"},"language":"en","primary_location":{"id":"doi:10.1007/s00332-022-09844-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-022-09844-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-022-09844-3.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s00332-022-09844-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058565648","display_name":"Seokjun Ham","orcid":"https://orcid.org/0000-0002-2917-312X"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Seokjun Ham","raw_affiliation_strings":["Department of Mathematics, Korea University, Seoul, 02841 Republic of Korea","Department of Mathematics, Korea University, Seoul, 02841, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Korea University, Seoul, 02841 Republic of Korea","institution_ids":["https://openalex.org/I197347611"]},{"raw_affiliation_string":"Department of Mathematics, Korea University, Seoul, 02841, Republic of Korea","institution_ids":["https://openalex.org/I197347611"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058269779","display_name":"Yibao Li","orcid":"https://orcid.org/0000-0002-4847-5430"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yibao Li","raw_affiliation_strings":["School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049 China","School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an, 710049, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049 China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an, 710049, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069818290","display_name":"Darae Jeong","orcid":"https://orcid.org/0000-0002-9931-1137"},"institutions":[{"id":"https://openalex.org/I165507594","display_name":"Kangwon National University","ror":"https://ror.org/01mh5ph17","country_code":"KR","type":"education","lineage":["https://openalex.org/I165507594"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Darae Jeong","raw_affiliation_strings":["Department of Mathematics, Kangwon National University, Gangwon-do, 24341 Republic of Korea","Department of Mathematics, Kangwon National University, Gangwon-do, 24341, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Kangwon National University, Gangwon-do, 24341 Republic of Korea","institution_ids":["https://openalex.org/I165507594"]},{"raw_affiliation_string":"Department of Mathematics, Kangwon National University, Gangwon-do, 24341, Republic of Korea","institution_ids":["https://openalex.org/I165507594"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101566848","display_name":"Chaeyoung Lee","orcid":"https://orcid.org/0000-0002-1120-2455"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Chaeyoung Lee","raw_affiliation_strings":["Department of Mathematics, Korea University, Seoul, 02841 Republic of Korea","Department of Mathematics, Korea University, Seoul, 02841, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Korea University, Seoul, 02841 Republic of Korea","institution_ids":["https://openalex.org/I197347611"]},{"raw_affiliation_string":"Department of Mathematics, Korea University, Seoul, 02841, Republic of Korea","institution_ids":["https://openalex.org/I197347611"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083693585","display_name":"Soobin Kwak","orcid":"https://orcid.org/0000-0001-7693-8992"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Soobin Kwak","raw_affiliation_strings":["Department of Mathematics, Korea University, Seoul, 02841 Republic of Korea","Department of Mathematics, Korea University, Seoul, 02841, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Korea University, Seoul, 02841 Republic of Korea","institution_ids":["https://openalex.org/I197347611"]},{"raw_affiliation_string":"Department of Mathematics, Korea University, Seoul, 02841, Republic of Korea","institution_ids":["https://openalex.org/I197347611"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101601090","display_name":"Youngjin Hwang","orcid":"https://orcid.org/0000-0002-6270-5386"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Youngjin Hwang","raw_affiliation_strings":["Department of Mathematics, Korea University, Seoul, 02841 Republic of Korea","Department of Mathematics, Korea University, Seoul, 02841, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Korea University, Seoul, 02841 Republic of Korea","institution_ids":["https://openalex.org/I197347611"]},{"raw_affiliation_string":"Department of Mathematics, Korea University, Seoul, 02841, Republic of Korea","institution_ids":["https://openalex.org/I197347611"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100698865","display_name":"Junseok Kim","orcid":"https://orcid.org/0000-0002-0484-9189"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Junseok Kim","raw_affiliation_strings":["Department of Mathematics, Korea University, Seoul, 02841 Republic of Korea","Department of Mathematics, Korea University, Seoul, 02841, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Korea University, Seoul, 02841 Republic of Korea","institution_ids":["https://openalex.org/I197347611"]},{"raw_affiliation_string":"Department of Mathematics, Korea University, Seoul, 02841, Republic of Korea","institution_ids":["https://openalex.org/I197347611"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5058565648"],"corresponding_institution_ids":["https://openalex.org/I197347611"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.0495,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.7329639,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"32","issue":"6","first_page":"80","last_page":"80"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9997000098228455,"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":0.9997000098228455,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9929999709129333,"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/T10670","display_name":"Aluminum Alloy Microstructure Properties","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/cahn\u2013hilliard-equation","display_name":"Cahn\u2013Hilliard equation","score":0.8764560222625732},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.642966628074646},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.625085711479187},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5073346495628357},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4891982078552246},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4841206967830658},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.4644218981266022},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4590936601161957},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4316946268081665},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3560602068901062},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.29120129346847534},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.104451984167099}],"concepts":[{"id":"https://openalex.org/C24822716","wikidata":"https://www.wikidata.org/wiki/Q5017440","display_name":"Cahn\u2013Hilliard equation","level":3,"score":0.8764560222625732},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.642966628074646},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.625085711479187},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5073346495628357},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4891982078552246},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4841206967830658},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.4644218981266022},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4590936601161957},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4316946268081665},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3560602068901062},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.29120129346847534},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.104451984167099},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00332-022-09844-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-022-09844-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-022-09844-3.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},{"id":"pmid:36089998","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36089998","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 nonlinear science","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:9444276","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9444276","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","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":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"J Nonlinear Sci","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s00332-022-09844-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-022-09844-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-022-09844-3.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G30685149","display_name":null,"funder_award_id":"BK21 FOUR","funder_id":"https://openalex.org/F4320320671","funder_display_name":"National Research Foundation"},{"id":"https://openalex.org/G4995453646","display_name":null,"funder_award_id":"BK21 FOUR","funder_id":"https://openalex.org/F4320321373","funder_display_name":"Korea University"},{"id":"https://openalex.org/G5905064654","display_name":null,"funder_award_id":"2019005","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G6125236940","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320321373","funder_display_name":"Korea University"},{"id":"https://openalex.org/G6482327896","display_name":null,"funder_award_id":"project BK21 FOUR","funder_id":"https://openalex.org/F4320320671","funder_display_name":"National Research Foundation"},{"id":"https://openalex.org/G7500379706","display_name":null,"funder_award_id":"XTR042019005","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G8951484681","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320321373","display_name":"Korea University","ror":"https://ror.org/047dqcg40"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4294653772.pdf"},"referenced_works_count":64,"referenced_works":["https://openalex.org/W1971518097","https://openalex.org/W2004825628","https://openalex.org/W2007925187","https://openalex.org/W2046528357","https://openalex.org/W2050638715","https://openalex.org/W2057366524","https://openalex.org/W2064468013","https://openalex.org/W2069257547","https://openalex.org/W2077047259","https://openalex.org/W2081932384","https://openalex.org/W2107746395","https://openalex.org/W2124994039","https://openalex.org/W2135478528","https://openalex.org/W2148146770","https://openalex.org/W2161620664","https://openalex.org/W2161952654","https://openalex.org/W2163526661","https://openalex.org/W2167347425","https://openalex.org/W2171628686","https://openalex.org/W2177852322","https://openalex.org/W2183709657","https://openalex.org/W2206898513","https://openalex.org/W2499761122","https://openalex.org/W2501163367","https://openalex.org/W2593432127","https://openalex.org/W2593562401","https://openalex.org/W2618364630","https://openalex.org/W2626341890","https://openalex.org/W2766919877","https://openalex.org/W2767124575","https://openalex.org/W2789307403","https://openalex.org/W2790424815","https://openalex.org/W2902106637","https://openalex.org/W2903512933","https://openalex.org/W2922030862","https://openalex.org/W2926865354","https://openalex.org/W2963024398","https://openalex.org/W2963334563","https://openalex.org/W2963533073","https://openalex.org/W2983925907","https://openalex.org/W2995360848","https://openalex.org/W2996828316","https://openalex.org/W3015453200","https://openalex.org/W3080439246","https://openalex.org/W3081421684","https://openalex.org/W3087775895","https://openalex.org/W3096953690","https://openalex.org/W3098765149","https://openalex.org/W3106376373","https://openalex.org/W3111579359","https://openalex.org/W3120045695","https://openalex.org/W3127600075","https://openalex.org/W3130226958","https://openalex.org/W3135531418","https://openalex.org/W3141285761","https://openalex.org/W3145247344","https://openalex.org/W3164143613","https://openalex.org/W3196123858","https://openalex.org/W3201706615","https://openalex.org/W3202743042","https://openalex.org/W4200481524","https://openalex.org/W4280529818","https://openalex.org/W4292169137","https://openalex.org/W4382891143"],"related_works":["https://openalex.org/W2330640442","https://openalex.org/W1975234065","https://openalex.org/W2392533133","https://openalex.org/W2617981106","https://openalex.org/W4251142058","https://openalex.org/W1965041963","https://openalex.org/W2007426143","https://openalex.org/W2384221708","https://openalex.org/W2171402820","https://openalex.org/W2526971967"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2026-03-16T09:10:04.655348","created_date":"2025-10-10T00:00:00"}
