{"id":"https://openalex.org/W4416893946","doi":"https://doi.org/10.1007/s10915-025-03142-2","title":"Optimal Error Estimates of the Semi-Discrete Local Discontinuous Galerkin Method and Large Time-Stepping Methods for the Square Phase Field Crystal Equation","display_name":"Optimal Error Estimates of the Semi-Discrete Local Discontinuous Galerkin Method and Large Time-Stepping Methods for the Square Phase Field Crystal Equation","publication_year":2025,"publication_date":"2025-12-02","ids":{"openalex":"https://openalex.org/W4416893946","doi":"https://doi.org/10.1007/s10915-025-03142-2"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-025-03142-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-025-03142-2","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/A5066692435","display_name":"Xiaolei Wu","orcid":null},"institutions":[{"id":"https://openalex.org/I38877650","display_name":"Zhengzhou University","ror":"https://ror.org/04ypx8c21","country_code":"CN","type":"education","lineage":["https://openalex.org/I38877650"]},{"id":"https://openalex.org/I4210094772","display_name":"Henan University of Engineering","ror":"https://ror.org/007wym039","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210094772"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xingzhuo Wu","raw_affiliation_strings":["School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan, 450001, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan, 450001, P.R. China","institution_ids":["https://openalex.org/I38877650","https://openalex.org/I4210094772"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010033208","display_name":"Ruihan Guo","orcid":"https://orcid.org/0000-0002-1687-5907"},"institutions":[{"id":"https://openalex.org/I38877650","display_name":"Zhengzhou University","ror":"https://ror.org/04ypx8c21","country_code":"CN","type":"education","lineage":["https://openalex.org/I38877650"]},{"id":"https://openalex.org/I4210094772","display_name":"Henan University of Engineering","ror":"https://ror.org/007wym039","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210094772"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ruihan Guo","raw_affiliation_strings":["School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan, 450001, P.R. China"],"raw_orcid":"https://orcid.org/0000-0002-1687-5907","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan, 450001, P.R. China","institution_ids":["https://openalex.org/I38877650","https://openalex.org/I4210094772"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5010033208"],"corresponding_institution_ids":["https://openalex.org/I38877650","https://openalex.org/I4210094772"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.3197,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.57895119,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"106","issue":"1","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":0.9746000170707703,"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":0.9746000170707703,"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":0.010599999688565731,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.003000000026077032,"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/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.8507000207901001},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7426000237464905},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.5928000211715698},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5830000042915344},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.4934999942779541},{"id":"https://openalex.org/keywords/phase-field-models","display_name":"Phase field models","score":0.4681999981403351},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.43470001220703125},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.43220001459121704}],"concepts":[{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.8507000207901001},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8245999813079834},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7426000237464905},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.5928000211715698},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5830000042915344},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5378000140190125},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.4934999942779541},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.483599990606308},{"id":"https://openalex.org/C2780568864","wikidata":"https://www.wikidata.org/wiki/Q1640482","display_name":"Phase field models","level":3,"score":0.4681999981403351},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.43470001220703125},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.43220001459121704},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4259999990463257},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.3862000107765198},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.3734000027179718},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.31189998984336853},{"id":"https://openalex.org/C2989268449","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Energy method","level":2,"score":0.2921000123023987},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C30295242","wikidata":"https://www.wikidata.org/wiki/Q1023483","display_name":"Courant\u2013Friedrichs\u2013Lewy condition","level":3,"score":0.27300000190734863},{"id":"https://openalex.org/C7356347","wikidata":"https://www.wikidata.org/wiki/Q1307838","display_name":"Unit square","level":2,"score":0.26429998874664307},{"id":"https://openalex.org/C2781285689","wikidata":"https://www.wikidata.org/wiki/Q21921428","display_name":"Crystal (programming language)","level":2,"score":0.26350000500679016}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-025-03142-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-025-03142-2","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/G2148519409","display_name":null,"funder_award_id":"252300421210","funder_id":"https://openalex.org/F4320323845","funder_display_name":"Natural Science Foundation of Henan Province"},{"id":"https://openalex.org/G4996507338","display_name":null,"funder_award_id":"12271492","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/F4320323845","display_name":"Natural Science Foundation of Henan Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1993923624","https://openalex.org/W2012938047","https://openalex.org/W2019066638","https://openalex.org/W2043017073","https://openalex.org/W2046134068","https://openalex.org/W2049937590","https://openalex.org/W2057366524","https://openalex.org/W2069036386","https://openalex.org/W2074622236","https://openalex.org/W2080928083","https://openalex.org/W2091319328","https://openalex.org/W2110990313","https://openalex.org/W2116282764","https://openalex.org/W2265162061","https://openalex.org/W2501163367","https://openalex.org/W2736147079","https://openalex.org/W2952204387","https://openalex.org/W2954429508","https://openalex.org/W3174720744","https://openalex.org/W4213415934","https://openalex.org/W4297141702","https://openalex.org/W4297475445","https://openalex.org/W4321486948","https://openalex.org/W4379196820","https://openalex.org/W4396921047","https://openalex.org/W4399445140"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-12-02T00:00:00"}
