{"id":"https://openalex.org/W4285089322","doi":"https://doi.org/10.1007/s10444-022-09961-3","title":"Unconditionally optimal error estimates of a linearized weak Galerkin finite element method for semilinear parabolic equations","display_name":"Unconditionally optimal error estimates of a linearized weak Galerkin finite element method for semilinear parabolic equations","publication_year":2022,"publication_date":"2022-07-12","ids":{"openalex":"https://openalex.org/W4285089322","doi":"https://doi.org/10.1007/s10444-022-09961-3"},"language":"en","primary_location":{"id":"doi:10.1007/s10444-022-09961-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10444-022-09961-3","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":"Advances in Computational 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/A5100414451","display_name":"Ying Liu","orcid":"https://orcid.org/0000-0003-3380-4243"},"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"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ying Liu","raw_affiliation_strings":["Research Center for Computational Science, School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, 710129, Shaanxi, China","Research Center for Computational Science, School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, 710129, Shaanxi, China"],"affiliations":[{"raw_affiliation_string":"Research Center for Computational Science, School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, 710129, Shaanxi, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"Research Center for Computational Science, School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, 710129, Shaanxi, China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018937994","display_name":"Zhen Guan","orcid":"https://orcid.org/0000-0001-5090-7004"},"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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhen Guan","raw_affiliation_strings":["Research Center for Computational Science, School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, 710129, Shaanxi, China","Research Center for Computational Science, School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, 710129, Shaanxi, China"],"affiliations":[{"raw_affiliation_string":"Research Center for Computational Science, School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, 710129, Shaanxi, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"Research Center for Computational Science, School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, 710129, Shaanxi, China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069200204","display_name":"Yufeng Nie","orcid":"https://orcid.org/0000-0001-7881-5806"},"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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yufeng Nie","raw_affiliation_strings":["Research Center for Computational Science, School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, 710129, Shaanxi, China","Research Center for Computational Science, School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, 710129, Shaanxi, China"],"affiliations":[{"raw_affiliation_string":"Research Center for Computational Science, School of Mathematics and Statistics, Northwestern Polytechnical University, Xi\u2019an, 710129, Shaanxi, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"Research Center for Computational Science, School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, 710129, Shaanxi, China","institution_ids":["https://openalex.org/I17145004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100414451"],"corresponding_institution_ids":["https://openalex.org/I17145004"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.6615,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.60977547,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"48","issue":"4","first_page":null,"last_page":null},"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":0.9998999834060669,"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":0.9998999834060669,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9988999962806702,"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":0.9965000152587891,"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":0.8190431594848633},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7524539232254028},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7379447221755981},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.6626259088516235},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.6592929363250732},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.644694447517395},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6386992931365967},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6318323612213135},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.5131157040596008},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5007655620574951},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4492541253566742},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.43534138798713684},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.42534902691841125},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.24404406547546387},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15460285544395447},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11372122168540955},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.053933680057525635}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8190431594848633},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7524539232254028},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7379447221755981},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.6626259088516235},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.6592929363250732},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.644694447517395},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6386992931365967},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6318323612213135},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.5131157040596008},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5007655620574951},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4492541253566742},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.43534138798713684},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.42534902691841125},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.24404406547546387},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15460285544395447},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11372122168540955},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.053933680057525635},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10444-022-09961-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10444-022-09961-3","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":"Advances in Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1724846330","display_name":null,"funder_award_id":"11971386","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":47,"referenced_works":["https://openalex.org/W862596102","https://openalex.org/W1967868847","https://openalex.org/W1970564873","https://openalex.org/W2004017120","https://openalex.org/W2019897249","https://openalex.org/W2022525937","https://openalex.org/W2036344137","https://openalex.org/W2039955529","https://openalex.org/W2047378168","https://openalex.org/W2051862019","https://openalex.org/W2080980858","https://openalex.org/W2287883979","https://openalex.org/W2299374223","https://openalex.org/W2435960546","https://openalex.org/W2437878828","https://openalex.org/W2512307835","https://openalex.org/W2534626330","https://openalex.org/W2558735048","https://openalex.org/W2561188040","https://openalex.org/W2593831893","https://openalex.org/W2746115620","https://openalex.org/W2770422933","https://openalex.org/W2778500870","https://openalex.org/W2782024549","https://openalex.org/W2792441096","https://openalex.org/W2799433743","https://openalex.org/W2805001116","https://openalex.org/W2895980198","https://openalex.org/W2941043721","https://openalex.org/W2947298668","https://openalex.org/W2962973556","https://openalex.org/W2963492535","https://openalex.org/W2981580059","https://openalex.org/W2993963782","https://openalex.org/W3023067440","https://openalex.org/W3100645514","https://openalex.org/W3110724176","https://openalex.org/W3128593186","https://openalex.org/W3134957668","https://openalex.org/W3139923052","https://openalex.org/W3154306992","https://openalex.org/W3194309593","https://openalex.org/W3205545207","https://openalex.org/W3211697879","https://openalex.org/W4223905103","https://openalex.org/W4232436772","https://openalex.org/W4238630926"],"related_works":["https://openalex.org/W2009711572","https://openalex.org/W2377834777","https://openalex.org/W1981367860","https://openalex.org/W2365810470","https://openalex.org/W1674877062","https://openalex.org/W2158188297","https://openalex.org/W4390271665","https://openalex.org/W2039043967","https://openalex.org/W2501406218","https://openalex.org/W2225139434"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}