{"id":"https://openalex.org/W4401554150","doi":"https://doi.org/10.1007/s11075-024-01910-z","title":"Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation","display_name":"Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation","publication_year":2024,"publication_date":"2024-08-13","ids":{"openalex":"https://openalex.org/W4401554150","doi":"https://doi.org/10.1007/s11075-024-01910-z"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-024-01910-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-024-01910-z","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","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/A5102723944","display_name":"Yaoyao Chen","orcid":"https://orcid.org/0009-0006-8897-5284"},"institutions":[{"id":"https://openalex.org/I4472751","display_name":"Anhui Normal University","ror":"https://ror.org/05fsfvw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I4472751"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yaoyao Chen","raw_affiliation_strings":["School of Mathematics and Statistics, Anhui Normal University, Wuhu, Anhui, 241000, PR China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Anhui Normal University, Wuhu, Anhui, 241000, PR China","institution_ids":["https://openalex.org/I4472751"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100713577","display_name":"Hailiang Liu","orcid":"https://orcid.org/0000-0003-3948-2150"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hailiang Liu","raw_affiliation_strings":["Department of Mathematics, Iowa State University, Ames, IA, 50011, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Iowa State University, Ames, IA, 50011, USA","institution_ids":["https://openalex.org/I173911158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020948241","display_name":"Nianyu Yi","orcid":"https://orcid.org/0000-0002-2106-8237"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Nianyu Yi","raw_affiliation_strings":["Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, 411105, P.R. China"],"affiliations":[{"raw_affiliation_string":"Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, 411105, P.R. China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010751299","display_name":"Peimeng Yin","orcid":"https://orcid.org/0000-0002-9188-8011"},"institutions":[{"id":"https://openalex.org/I164936912","display_name":"The University of Texas at El Paso","ror":"https://ror.org/04d5vba33","country_code":"US","type":"education","lineage":["https://openalex.org/I164936912"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Peimeng Yin","raw_affiliation_strings":["Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, USA","institution_ids":["https://openalex.org/I164936912"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5010751299"],"corresponding_institution_ids":["https://openalex.org/I164936912"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.85,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.74817349,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"99","issue":"3","first_page":"1161","last_page":"1202"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9965000152587891,"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":0.9944000244140625,"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":0.8158525228500366},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7325615882873535},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7088949680328369},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7044800519943237},{"id":"https://openalex.org/keywords/allen\u2013cahn-equation","display_name":"Allen\u2013Cahn equation","score":0.6986174583435059},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6758304238319397},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5145118236541748},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.46914854645729065},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44029274582862854},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.42158183455467224},{"id":"https://openalex.org/keywords/energy-conservation","display_name":"Energy conservation","score":0.4195367097854614},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41414594650268555},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.3670384883880615},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11569064855575562}],"concepts":[{"id":"https://openalex.org/C24822716","wikidata":"https://www.wikidata.org/wiki/Q5017440","display_name":"Cahn\u2013Hilliard equation","level":3,"score":0.8158525228500366},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7325615882873535},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7088949680328369},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7044800519943237},{"id":"https://openalex.org/C2777166216","wikidata":"https://www.wikidata.org/wiki/Q4732089","display_name":"Allen\u2013Cahn equation","level":2,"score":0.6986174583435059},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6758304238319397},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5145118236541748},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.46914854645729065},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44029274582862854},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.42158183455467224},{"id":"https://openalex.org/C520301825","wikidata":"https://www.wikidata.org/wiki/Q380170","display_name":"Energy conservation","level":2,"score":0.4195367097854614},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41414594650268555},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3670384883880615},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11569064855575562},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-024-01910-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-024-01910-z","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.7900000214576721,"id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G1650270860","display_name":null,"funder_award_id":"2022AH040027","funder_id":"https://openalex.org/F4320335406","funder_display_name":"University Natural Science Research Project of Anhui Province"},{"id":"https://openalex.org/G2550842853","display_name":null,"funder_award_id":"12071400","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2909011478","display_name":null,"funder_award_id":"2020YFA0713500","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G3778909633","display_name":null,"funder_award_id":"12201010","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335406","display_name":"University Natural Science Research Project of Anhui Province","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W1525717382","https://openalex.org/W1933093983","https://openalex.org/W1963865657","https://openalex.org/W1966584387","https://openalex.org/W1969100313","https://openalex.org/W1991970712","https://openalex.org/W1992445851","https://openalex.org/W2030113746","https://openalex.org/W2046528357","https://openalex.org/W2048876667","https://openalex.org/W2050969603","https://openalex.org/W2054766104","https://openalex.org/W2062245988","https://openalex.org/W2062738010","https://openalex.org/W2063201396","https://openalex.org/W2080928083","https://openalex.org/W2124612352","https://openalex.org/W2128204029","https://openalex.org/W2138026128","https://openalex.org/W2550726378","https://openalex.org/W2593562401","https://openalex.org/W2766149883","https://openalex.org/W2808330254","https://openalex.org/W2918504611","https://openalex.org/W2962689056","https://openalex.org/W2962906715","https://openalex.org/W2963236482","https://openalex.org/W2964580220","https://openalex.org/W2969892102","https://openalex.org/W2983445643","https://openalex.org/W2994711561","https://openalex.org/W3014054560","https://openalex.org/W3099699133","https://openalex.org/W3104136857","https://openalex.org/W3105973590","https://openalex.org/W4206208254","https://openalex.org/W4220801429","https://openalex.org/W4229032134","https://openalex.org/W4303644478","https://openalex.org/W4390540575"],"related_works":["https://openalex.org/W4388722486","https://openalex.org/W346508299","https://openalex.org/W1980263572","https://openalex.org/W1488888950","https://openalex.org/W2343104825","https://openalex.org/W3182767157","https://openalex.org/W4385263414","https://openalex.org/W4300921184","https://openalex.org/W2948924069","https://openalex.org/W2605241284"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
