{"id":"https://openalex.org/W4411476525","doi":"https://doi.org/10.1016/j.cam.2025.116849","title":"Optimal error estimates of the local discontinuous Galerkin method and high-order energy stable RK-SAV scheme for the phase field crystal equation","display_name":"Optimal error estimates of the local discontinuous Galerkin method and high-order energy stable RK-SAV scheme for the phase field crystal equation","publication_year":2025,"publication_date":"2025-06-20","ids":{"openalex":"https://openalex.org/W4411476525","doi":"https://doi.org/10.1016/j.cam.2025.116849"},"language":"en","primary_location":{"id":"doi:10.1016/j.cam.2025.116849","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.cam.2025.116849","pdf_url":null,"source":{"id":"https://openalex.org/S165473669","display_name":"Journal of Computational and Applied Mathematics","issn_l":"0377-0427","issn":["0377-0427","1879-1778"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Applied Mathematics","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/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"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ruihan Guo","raw_affiliation_strings":["School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, Henan, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, Henan, PR China","institution_ids":["https://openalex.org/I38877650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100302130","display_name":"Yuqing Yan","orcid":"https://orcid.org/0009-0002-4436-0545"},"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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuqing Yan","raw_affiliation_strings":["School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, Henan, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, Henan, PR China","institution_ids":["https://openalex.org/I38877650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100765474","display_name":"Xiaobin Liu","orcid":"https://orcid.org/0009-0000-5630-2700"},"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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaobin Liu","raw_affiliation_strings":["School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, Henan, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, Henan, PR China","institution_ids":["https://openalex.org/I38877650"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010033208"],"corresponding_institution_ids":["https://openalex.org/I38877650"],"apc_list":{"value":3040,"currency":"USD","value_usd":3040},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07785823,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"473","issue":null,"first_page":"116849","last_page":"116849"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9972000122070312,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9033322930335999},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5444763898849487},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5199188590049744},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5074991583824158},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4990968704223633},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.4707679748535156},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.464423805475235},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4570882022380829},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4135516285896301},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14429500699043274},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11556711792945862},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11105048656463623},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07825633883476257}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9033322930335999},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5444763898849487},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5199188590049744},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5074991583824158},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4990968704223633},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.4707679748535156},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.464423805475235},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4570882022380829},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4135516285896301},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14429500699043274},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11556711792945862},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11105048656463623},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07825633883476257},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.cam.2025.116849","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.cam.2025.116849","pdf_url":null,"source":{"id":"https://openalex.org/S165473669","display_name":"Journal of Computational and Applied Mathematics","issn_l":"0377-0427","issn":["0377-0427","1879-1778"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.75,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G312338971","display_name":null,"funder_award_id":"252300420322","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/F4320322866","display_name":"Natural Science Foundation of Hainan Province","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":20,"referenced_works":["https://openalex.org/W49087508","https://openalex.org/W1509923322","https://openalex.org/W1979546093","https://openalex.org/W2000883601","https://openalex.org/W2012938047","https://openalex.org/W2029449803","https://openalex.org/W2057808716","https://openalex.org/W2069036386","https://openalex.org/W2074622236","https://openalex.org/W2265162061","https://openalex.org/W2297827206","https://openalex.org/W2736147079","https://openalex.org/W2913992843","https://openalex.org/W3011217598","https://openalex.org/W3031773824","https://openalex.org/W3081510208","https://openalex.org/W3159144148","https://openalex.org/W4210300254","https://openalex.org/W4297475445","https://openalex.org/W4391532981"],"related_works":["https://openalex.org/W1975289146","https://openalex.org/W2124287120","https://openalex.org/W1951249712","https://openalex.org/W2105887828","https://openalex.org/W2314373002","https://openalex.org/W2351235964","https://openalex.org/W2122599759","https://openalex.org/W4236520801","https://openalex.org/W2334267221","https://openalex.org/W4238937692"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-10-10T00:00:00"}
