{"id":"https://openalex.org/W2055271100","doi":"https://doi.org/10.1090/s0025-5718-2013-02703-2","title":"Mesh dependent stability and condition number estimates for finite element approximations of parabolic problems","display_name":"Mesh dependent stability and condition number estimates for finite element approximations of parabolic problems","publication_year":2013,"publication_date":"2013-05-02","ids":{"openalex":"https://openalex.org/W2055271100","doi":"https://doi.org/10.1090/s0025-5718-2013-02703-2","mag":"2055271100"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2013-02703-2","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2013-02703-2","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","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/A5102264162","display_name":"Liyong Zhu","orcid":"https://orcid.org/0000-0002-5126-8504"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liyong Zhu","raw_affiliation_strings":["LMIB and School of Mathematics and Systems Sciences, Beihang University, 100191, Beijing, People\u00e2\u0080\u0099s Republic of China","LMIB and School of Mathematics and Systems Sciences, Beihang University, 100191, Beijing, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LMIB and School of Mathematics and Systems Sciences, Beihang University, 100191, Beijing, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"LMIB and School of Mathematics and Systems Sciences, Beihang University, 100191, Beijing, People\u2019s Republic of China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056115552","display_name":"Qiang Du","orcid":"https://orcid.org/0000-0002-1067-8937"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qiang Du","raw_affiliation_strings":["Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802","Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802#TAB#","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3721,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.80703619,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"83","issue":"285","first_page":"37","last_page":"64"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9972000122070312,"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/polygon-mesh","display_name":"Polygon mesh","score":0.8386549949645996},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8304876685142517},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.76360684633255},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.749004602432251},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6123881936073303},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.585585355758667},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5214238166809082},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.45253026485443115},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3693612813949585},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18124225735664368},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09884926676750183}],"concepts":[{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.8386549949645996},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8304876685142517},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.76360684633255},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.749004602432251},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6123881936073303},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.585585355758667},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5214238166809082},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.45253026485443115},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3693612813949585},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18124225735664368},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09884926676750183},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-2013-02703-2","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2013-02703-2","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W118271839","https://openalex.org/W1492326914","https://openalex.org/W1969206886","https://openalex.org/W1983972632","https://openalex.org/W2004719710","https://openalex.org/W2022527567","https://openalex.org/W2030982479","https://openalex.org/W2032916960","https://openalex.org/W2033086891","https://openalex.org/W2038162840","https://openalex.org/W2044355921","https://openalex.org/W2046756012","https://openalex.org/W2049914863","https://openalex.org/W2055441679","https://openalex.org/W2059680655","https://openalex.org/W2061253771","https://openalex.org/W2067603545","https://openalex.org/W2082388745","https://openalex.org/W2082621526","https://openalex.org/W2085077600","https://openalex.org/W2102779916","https://openalex.org/W2121613024","https://openalex.org/W2134719842","https://openalex.org/W2155513349","https://openalex.org/W4238784554"],"related_works":["https://openalex.org/W2965585506","https://openalex.org/W3090384263","https://openalex.org/W2796969560","https://openalex.org/W4252583622","https://openalex.org/W2087757951","https://openalex.org/W2149298118","https://openalex.org/W2950383035","https://openalex.org/W2791967325","https://openalex.org/W4299794286","https://openalex.org/W2556186148"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,59],"discuss":[4],"the":[5,12,15,42,68,90,100,105,117],"effects":[6],"of":[7,17,21,50,99,104,119],"spatial":[8],"simplicial":[9,57],"meshes":[10],"on":[11,41,47,81,86],"stability":[13,121],"and":[14],"conditioning":[16],"fully":[18],"discrete":[19],"approximations":[20],"a":[22,26,61],"parabolic":[23,123],"equation":[24],"using":[25,126],"general":[27,51],"finite":[28,52],"element":[29,53],"discretization":[30],"in":[31,38],"space":[32],"with":[33],"explicit":[34,69,96],"or":[35],"implicit":[36,91],"marching":[37],"time.":[39],"Based":[40],"new":[43,62],"mesh":[44,82,87],"dependent":[45],"bounds":[46],"extreme":[48],"eigenvalues":[49],"systems":[54,108],"defined":[55],"for":[56,67,122],"meshes,":[58],"derive":[60],"time":[63,70,92],"step":[64],"size":[65,83],"condition":[66,102],"integration":[71,93],"schemes":[72],"presented,":[73],"which":[74],"provides":[75],"more":[76],"precise":[77],"dependence":[78],"not":[79],"only":[80],"but":[84],"also":[85,110],"shape.":[88],"For":[89],"schemes,":[94],"some":[95],"mesh-dependent":[97],"estimates":[98],"spectral":[101],"number":[103],"resulting":[106],"linear":[107],"are":[109],"established.":[111],"Our":[112],"results":[113],"provide":[114],"guidance":[115],"to":[116],"studies":[118],"numerical":[120],"problems":[124],"when":[125],"spatially":[127],"unstructured":[128],"adaptive":[129],"and/or":[130],"possibly":[131],"anisotropic":[132],"meshes.":[133]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
