{"id":"https://openalex.org/W4385685797","doi":"https://doi.org/10.1007/s11075-023-01635-5","title":"Adaptive discontinuous Galerkin finite element methods for the Allen-Cahn equation on polygonal meshes","display_name":"Adaptive discontinuous Galerkin finite element methods for the Allen-Cahn equation on polygonal meshes","publication_year":2023,"publication_date":"2023-08-10","ids":{"openalex":"https://openalex.org/W4385685797","doi":"https://doi.org/10.1007/s11075-023-01635-5"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-023-01635-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-023-01635-5","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/A5114195951","display_name":"Rui Li","orcid":"https://orcid.org/0000-0002-6105-1894"},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rui Li","raw_affiliation_strings":["School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an, 710062, People\u2019s Republic of China","School of Mathematics and Statistics, Shaanxi Normal University, Xi'an, 710062, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an, 710062, People\u2019s Republic of China","institution_ids":["https://openalex.org/I88830068"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Shaanxi Normal University, Xi'an, 710062, People's Republic of China","institution_ids":["https://openalex.org/I88830068"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026611351","display_name":"Yali Gao","orcid":"https://orcid.org/0000-0001-8308-2475"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]},{"id":"https://openalex.org/I182722699","display_name":"Shenzhen Polytechnic University","ror":"https://ror.org/00d2w9g53","country_code":"CN","type":"education","lineage":["https://openalex.org/I182722699"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yali Gao","raw_affiliation_strings":["Research & Development Institute of Northwestern Polytechnical University in Shenzhen, Shenzhen, 518063, People\u2019s Republic of China","School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, 710129, People\u2019s Republic of China","School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, 710129, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research & Development Institute of Northwestern Polytechnical University in Shenzhen, Shenzhen, 518063, People\u2019s Republic of China","institution_ids":["https://openalex.org/I17145004","https://openalex.org/I182722699"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, 710129, People\u2019s Republic of China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, 710129, People's Republic of China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086480330","display_name":"Zhangxin Chen","orcid":"https://orcid.org/0000-0002-9107-1925"},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Zhangxin Chen","raw_affiliation_strings":["Department of Chemical & Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive N.W., Calgary, Alberta T2N 1N4, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical & Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive N.W., Calgary, Alberta T2N 1N4, Canada","institution_ids":["https://openalex.org/I168635309"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5026611351"],"corresponding_institution_ids":["https://openalex.org/I17145004","https://openalex.org/I182722699"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":2.2695,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.87518825,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"95","issue":"4","first_page":"1981","last_page":"2014"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9987000226974487,"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9987000226974487,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.6792688965797424},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6678413152694702},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.644895613193512},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6293764710426331},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.5806511640548706},{"id":"https://openalex.org/keywords/allen\u2013cahn-equation","display_name":"Allen\u2013Cahn equation","score":0.5527556538581848},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5488923788070679},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.44403499364852905},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.44087687134742737},{"id":"https://openalex.org/keywords/mesh-generation","display_name":"Mesh generation","score":0.4349583685398102},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37978872656822205},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3757379949092865},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3648235499858856},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3492218852043152}],"concepts":[{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.6792688965797424},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6678413152694702},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.644895613193512},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6293764710426331},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5806511640548706},{"id":"https://openalex.org/C2777166216","wikidata":"https://www.wikidata.org/wiki/Q4732089","display_name":"Allen\u2013Cahn equation","level":2,"score":0.5527556538581848},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5488923788070679},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.44403499364852905},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.44087687134742737},{"id":"https://openalex.org/C181145010","wikidata":"https://www.wikidata.org/wiki/Q4418033","display_name":"Mesh generation","level":3,"score":0.4349583685398102},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37978872656822205},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3757379949092865},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3648235499858856},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3492218852043152},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-023-01635-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-023-01635-5","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","id":"https://metadata.un.org/sdg/7","score":0.8500000238418579}],"awards":[{"id":"https://openalex.org/G2413793559","display_name":null,"funder_award_id":"11901461","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4490502468","display_name":null,"funder_award_id":"2020JQ-403","funder_id":"https://openalex.org/F4320324173","funder_display_name":"Natural Science Foundation of Shaanxi Province"},{"id":"https://openalex.org/G6400785960","display_name":null,"funder_award_id":"2020M673464","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G7920084","display_name":null,"funder_award_id":"2023A1515010697","funder_id":"https://openalex.org/F4320337111","funder_display_name":"Basic and Applied Basic Research Foundation of Guangdong Province"},{"id":"https://openalex.org/G8220571664","display_name":null,"funder_award_id":"11901372","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320312823","display_name":"CMG Reservoir Simulation Foundation","ror":"https://ror.org/013hjnc74"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320324173","display_name":"Natural Science Foundation of Shaanxi Province","ror":null},{"id":"https://openalex.org/F4320337111","display_name":"Basic and Applied Basic Research Foundation of Guangdong Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":129,"referenced_works":["https://openalex.org/W1560055494","https://openalex.org/W1566292686","https://openalex.org/W1790345590","https://openalex.org/W1920690606","https://openalex.org/W1950919561","https://openalex.org/W1963865657","https://openalex.org/W1966584387","https://openalex.org/W1967577632","https://openalex.org/W1969674427","https://openalex.org/W1975968248","https://openalex.org/W1990969719","https://openalex.org/W2000756381","https://openalex.org/W2008365488","https://openalex.org/W2031832209","https://openalex.org/W2035346182","https://openalex.org/W2038495454","https://openalex.org/W2041968314","https://openalex.org/W2046528357","https://openalex.org/W2050540280","https://openalex.org/W2050969603","https://openalex.org/W2053051937","https://openalex.org/W2062245988","https://openalex.org/W2064540445","https://openalex.org/W2066036475","https://openalex.org/W2072060492","https://openalex.org/W2073237186","https://openalex.org/W2086365560","https://openalex.org/W2099834786","https://openalex.org/W2111450821","https://openalex.org/W2115473334","https://openalex.org/W2116404756","https://openalex.org/W2130350269","https://openalex.org/W2133899315","https://openalex.org/W2141942500","https://openalex.org/W2144751639","https://openalex.org/W2146359766","https://openalex.org/W2165075232","https://openalex.org/W2166765763","https://openalex.org/W2172029033","https://openalex.org/W2300243767","https://openalex.org/W2312832458","https://openalex.org/W2313044839","https://openalex.org/W2327646252","https://openalex.org/W2334286307","https://openalex.org/W2407742808","https://openalex.org/W2415576848","https://openalex.org/W2416051874","https://openalex.org/W2462318036","https://openalex.org/W2471970532","https://openalex.org/W2507484451","https://openalex.org/W2510227433","https://openalex.org/W2523228639","https://openalex.org/W2531774840","https://openalex.org/W2550726378","https://openalex.org/W2562132457","https://openalex.org/W2589656637","https://openalex.org/W2607356190","https://openalex.org/W2737672067","https://openalex.org/W2740048351","https://openalex.org/W2756254807","https://openalex.org/W2766149883","https://openalex.org/W2784357211","https://openalex.org/W2790125671","https://openalex.org/W2793378113","https://openalex.org/W2793901947","https://openalex.org/W2807807213","https://openalex.org/W2883279833","https://openalex.org/W2887880955","https://openalex.org/W2889483471","https://openalex.org/W2893622182","https://openalex.org/W2902106637","https://openalex.org/W2902643746","https://openalex.org/W2907521988","https://openalex.org/W2909584443","https://openalex.org/W2917092178","https://openalex.org/W2922002644","https://openalex.org/W2926294467","https://openalex.org/W2953439596","https://openalex.org/W2962689056","https://openalex.org/W2962814658","https://openalex.org/W2963134446","https://openalex.org/W2963333235","https://openalex.org/W2963334563","https://openalex.org/W2963487886","https://openalex.org/W2963689320","https://openalex.org/W2963832984","https://openalex.org/W2964035458","https://openalex.org/W2964580220","https://openalex.org/W2966020116","https://openalex.org/W2969382357","https://openalex.org/W2976972080","https://openalex.org/W2990423170","https://openalex.org/W2990608730","https://openalex.org/W2998897266","https://openalex.org/W2999568010","https://openalex.org/W3004742603","https://openalex.org/W3006221137","https://openalex.org/W3007637113","https://openalex.org/W3008420272","https://openalex.org/W3012062350","https://openalex.org/W3014054560","https://openalex.org/W3021580541","https://openalex.org/W3023103662","https://openalex.org/W3031773824","https://openalex.org/W3033329645","https://openalex.org/W3038322078","https://openalex.org/W3039904202","https://openalex.org/W3048822804","https://openalex.org/W3080795262","https://openalex.org/W3099559215","https://openalex.org/W3126700533","https://openalex.org/W3131594322","https://openalex.org/W3131933093","https://openalex.org/W3151487737","https://openalex.org/W3166671318","https://openalex.org/W3179881989","https://openalex.org/W3190827300","https://openalex.org/W3191312318","https://openalex.org/W3193893684","https://openalex.org/W3198551377","https://openalex.org/W3216048531","https://openalex.org/W4200015933","https://openalex.org/W4200483882","https://openalex.org/W4226168322","https://openalex.org/W4233665781","https://openalex.org/W4293028925","https://openalex.org/W4317486266","https://openalex.org/W4365385307","https://openalex.org/W4379520773"],"related_works":["https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2887215440","https://openalex.org/W4250296811","https://openalex.org/W2103925787","https://openalex.org/W2377834777","https://openalex.org/W1562558505","https://openalex.org/W4390271665","https://openalex.org/W1965469317","https://openalex.org/W2069866412"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":3}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
