{"id":"https://openalex.org/W4414650323","doi":"https://doi.org/10.1007/s10915-025-03077-8","title":"Energy Dissipation Law and Maximum Bound Principle-Preserving Linear BDF2 Schemes with Variable Steps for the Allen\u2013Cahn Equation","display_name":"Energy Dissipation Law and Maximum Bound Principle-Preserving Linear BDF2 Schemes with Variable Steps for the Allen\u2013Cahn Equation","publication_year":2025,"publication_date":"2025-09-30","ids":{"openalex":"https://openalex.org/W4414650323","doi":"https://doi.org/10.1007/s10915-025-03077-8"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-025-03077-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-025-03077-8","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of 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/A5062391035","display_name":"Bingyin Zhang","orcid":"https://orcid.org/0000-0003-1298-3457"},"institutions":[{"id":"https://openalex.org/I59028903","display_name":"Ocean University of China","ror":"https://ror.org/04rdtx186","country_code":"CN","type":"education","lineage":["https://openalex.org/I59028903"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bingyin Zhang","raw_affiliation_strings":["School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, Shandong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, Shandong, China","institution_ids":["https://openalex.org/I59028903"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005603712","display_name":"Hongfei Fu","orcid":"https://orcid.org/0000-0002-8294-8086"},"institutions":[{"id":"https://openalex.org/I59028903","display_name":"Ocean University of China","ror":"https://ror.org/04rdtx186","country_code":"CN","type":"education","lineage":["https://openalex.org/I59028903"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongfei Fu","raw_affiliation_strings":["Laboratory of Marine Mathematics, Ocean University of China, Qingdao, 266100, Shandong, China","School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, Shandong, China"],"raw_orcid":"https://orcid.org/0000-0002-8294-8086","affiliations":[{"raw_affiliation_string":"Laboratory of Marine Mathematics, Ocean University of China, Qingdao, 266100, Shandong, China","institution_ids":["https://openalex.org/I59028903"]},{"raw_affiliation_string":"School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, Shandong, China","institution_ids":["https://openalex.org/I59028903"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015240471","display_name":"Rihui Lan","orcid":"https://orcid.org/0000-0002-6898-9164"},"institutions":[{"id":"https://openalex.org/I59028903","display_name":"Ocean University of China","ror":"https://ror.org/04rdtx186","country_code":"CN","type":"education","lineage":["https://openalex.org/I59028903"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rihui Lan","raw_affiliation_strings":["Laboratory of Marine Mathematics, Ocean University of China, Qingdao, 266100, Shandong, China","School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, Shandong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Marine Mathematics, Ocean University of China, Qingdao, 266100, Shandong, China","institution_ids":["https://openalex.org/I59028903"]},{"raw_affiliation_string":"School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, Shandong, China","institution_ids":["https://openalex.org/I59028903"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025983381","display_name":"Shusen Xie","orcid":"https://orcid.org/0000-0001-7039-2298"},"institutions":[{"id":"https://openalex.org/I59028903","display_name":"Ocean University of China","ror":"https://ror.org/04rdtx186","country_code":"CN","type":"education","lineage":["https://openalex.org/I59028903"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shusen Xie","raw_affiliation_strings":["Laboratory of Marine Mathematics, Ocean University of China, Qingdao, 266100, Shandong, China","School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, Shandong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Marine Mathematics, Ocean University of China, Qingdao, 266100, Shandong, China","institution_ids":["https://openalex.org/I59028903"]},{"raw_affiliation_string":"School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, Shandong, China","institution_ids":["https://openalex.org/I59028903"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5062391035"],"corresponding_institution_ids":["https://openalex.org/I59028903"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.19055151,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"105","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9995999932289124,"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":0.9995999932289124,"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/T12202","display_name":"nanoparticles nucleation surface interactions","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10413","display_name":"High-pressure geophysics and materials","score":0.9708999991416931,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.7124000191688538},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5889000296592712},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5189999938011169},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4575999975204468},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.45730000734329224},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.45419999957084656},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.43070000410079956},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4052000045776367}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8633999824523926},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.7124000191688538},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5889000296592712},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.527999997138977},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5189999938011169},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4575999975204468},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.45730000734329224},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.45419999957084656},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.43070000410079956},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4052000045776367},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.38260000944137573},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3580999970436096},{"id":"https://openalex.org/C152522140","wikidata":"https://www.wikidata.org/wiki/Q795746","display_name":"Backward differentiation formula","level":5,"score":0.3495999872684479},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.3402000069618225},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3395000100135803},{"id":"https://openalex.org/C20050597","wikidata":"https://www.wikidata.org/wiki/Q261527","display_name":"Linear form","level":2,"score":0.33820000290870667},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3296999931335449},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.3068000078201294},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3001999855041504},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.299699991941452},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2793000042438507},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C180188523","wikidata":"https://www.wikidata.org/wiki/Q574576","display_name":"Exponential decay","level":2,"score":0.2590000033378601}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-025-03077-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-025-03077-8","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1054713308","display_name":null,"funder_award_id":"12131014","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G385009835","display_name":null,"funder_award_id":"12371412","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8791341196","display_name":null,"funder_award_id":"12301531","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1977638711","https://openalex.org/W2030940697","https://openalex.org/W2036088969","https://openalex.org/W2037963783","https://openalex.org/W2041001120","https://openalex.org/W2050969603","https://openalex.org/W2052197429","https://openalex.org/W2077001143","https://openalex.org/W2080928083","https://openalex.org/W2083629653","https://openalex.org/W2117453669","https://openalex.org/W2128204029","https://openalex.org/W2507484451","https://openalex.org/W2511264644","https://openalex.org/W2526298107","https://openalex.org/W2588054282","https://openalex.org/W2766149883","https://openalex.org/W2893622182","https://openalex.org/W2914074116","https://openalex.org/W2917228799","https://openalex.org/W2964580220","https://openalex.org/W2991443752","https://openalex.org/W3024213355","https://openalex.org/W3046790868","https://openalex.org/W3048822804","https://openalex.org/W3080795262","https://openalex.org/W3110724176","https://openalex.org/W3135371133","https://openalex.org/W3151605865","https://openalex.org/W3159813613","https://openalex.org/W4205996846","https://openalex.org/W4213351654","https://openalex.org/W4225659843","https://openalex.org/W4284894622","https://openalex.org/W4284960277","https://openalex.org/W4306631595","https://openalex.org/W4313656479","https://openalex.org/W4318219130","https://openalex.org/W4324354753","https://openalex.org/W4327589968","https://openalex.org/W4391304299","https://openalex.org/W4395013751","https://openalex.org/W4400142805","https://openalex.org/W4405355810"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
