{"id":"https://openalex.org/W2088485015","doi":"https://doi.org/10.1090/s0025-5718-2013-02708-1","title":"A posteriori error analysis of finite element method for linear nonlocal diffusion and peridynamic models","display_name":"A posteriori error analysis of finite element method for linear nonlocal diffusion and peridynamic models","publication_year":2013,"publication_date":"2013-05-08","ids":{"openalex":"https://openalex.org/W2088485015","doi":"https://doi.org/10.1090/s0025-5718-2013-02708-1","mag":"2088485015"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2013-02708-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2013-02708-1","pdf_url":"https://www.ams.org/mcom/2013-82-284/S0025-5718-2013-02708-1/S0025-5718-2013-02708-1.pdf","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":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2013-82-284/S0025-5718-2013-02708-1/S0025-5718-2013-02708-1.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","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"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076382628","display_name":"Lili Ju","orcid":"https://orcid.org/0000-0002-6520-582X"},"institutions":[{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lili Ju","raw_affiliation_strings":["Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208","Department of Mathematics; University of South Carolina; Columbia South Carolina 29208"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208","institution_ids":["https://openalex.org/I155781252"]},{"raw_affiliation_string":"Department of Mathematics; University of South Carolina; Columbia South Carolina 29208","institution_ids":["https://openalex.org/I155781252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101684109","display_name":"Li Tian","orcid":"https://orcid.org/0000-0003-4425-0637"},"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":"Li Tian","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"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100722039","display_name":"Kun Zhou","orcid":"https://orcid.org/0000-0001-7660-2911"},"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":"Kun Zhou","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":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":15.8513,"has_fulltext":true,"cited_by_count":81,"citation_normalized_percentile":{"value":0.99507595,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"82","issue":"284","first_page":"1889","last_page":"1922"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9995999932289124,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.8464698791503906},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.8347464799880981},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7475801110267639},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.67242830991745},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6163192391395569},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.45428466796875},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.45368918776512146},{"id":"https://openalex.org/keywords/frame","display_name":"Frame (networking)","score":0.45224133133888245},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4364796578884125},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.41573649644851685},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.41162747144699097},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23638573288917542},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1467554271221161},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08203214406967163}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.8464698791503906},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.8347464799880981},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7475801110267639},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.67242830991745},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6163192391395569},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.45428466796875},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.45368918776512146},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.45224133133888245},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4364796578884125},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.41573649644851685},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.41162747144699097},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23638573288917542},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1467554271221161},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08203214406967163},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-2013-02708-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2013-02708-1","pdf_url":"https://www.ams.org/mcom/2013-82-284/S0025-5718-2013-02708-1/S0025-5718-2013-02708-1.pdf","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":{"id":"doi:10.1090/s0025-5718-2013-02708-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2013-02708-1","pdf_url":"https://www.ams.org/mcom/2013-82-284/S0025-5718-2013-02708-1/S0025-5718-2013-02708-1.pdf","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8684533629","display_name":"Mathematical and Computational Studies of Interfaces and Defects","funder_award_id":"1016073","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2088485015.pdf","grobid_xml":"https://content.openalex.org/works/W2088485015.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W174340818","https://openalex.org/W584420409","https://openalex.org/W1969333017","https://openalex.org/W1972827504","https://openalex.org/W1973127220","https://openalex.org/W1974725498","https://openalex.org/W1977835576","https://openalex.org/W1985849851","https://openalex.org/W1989125332","https://openalex.org/W1989594010","https://openalex.org/W1993193430","https://openalex.org/W1995404822","https://openalex.org/W2000897527","https://openalex.org/W2001730319","https://openalex.org/W2007393042","https://openalex.org/W2008086878","https://openalex.org/W2011884938","https://openalex.org/W2012828992","https://openalex.org/W2016094849","https://openalex.org/W2019591548","https://openalex.org/W2023102307","https://openalex.org/W2029529153","https://openalex.org/W2036587683","https://openalex.org/W2036662074","https://openalex.org/W2053482768","https://openalex.org/W2064845551","https://openalex.org/W2066970061","https://openalex.org/W2071036364","https://openalex.org/W2071636135","https://openalex.org/W2076206883","https://openalex.org/W2079626492","https://openalex.org/W2092047978","https://openalex.org/W2122602456","https://openalex.org/W2139045013","https://openalex.org/W2143206135","https://openalex.org/W2147986358","https://openalex.org/W2151889667","https://openalex.org/W2163377433","https://openalex.org/W2477542318","https://openalex.org/W2505585705","https://openalex.org/W2610905972","https://openalex.org/W2620978636","https://openalex.org/W2757176315","https://openalex.org/W4244509614","https://openalex.org/W4248748480","https://openalex.org/W6631823305"],"related_works":["https://openalex.org/W1974056099","https://openalex.org/W4287880334","https://openalex.org/W2386077341","https://openalex.org/W563589758","https://openalex.org/W4299447939","https://openalex.org/W2610540941","https://openalex.org/W2332908959","https://openalex.org/W3007553996","https://openalex.org/W1981407372","https://openalex.org/W2023658642"],"abstract_inverted_index":{"In":[0,25],"this":[1],"paper,":[2],"we":[3,27],"present":[4],"some":[5],"results":[6],"on":[7],"a":[8,31,37,64],"posteriori":[9,38,46,65],"error":[10,39,47,66],"analysis":[11,40],"of":[12,41,56],"finite":[13,76],"element":[14,77],"methods":[15],"for":[16,36],"solving":[17],"linear":[18],"nonlocal":[19,63],"diffusion":[20],"and":[21,54,68],"bond-based":[22],"peridynamic":[23,43],"models.":[24],"particular,":[26],"aim":[28],"to":[29,85],"propose":[30],"general":[32],"abstract":[33],"frame":[34],"work":[35],"the":[42,52,57,87],"problems.":[44],"A":[45],"estimators":[48,58],"are":[49,59,72,82],"consequently":[50],"prompted,":[51],"reliability":[53],"efficiency":[55],"proved.":[60],"Connections":[61],"between":[62],"estimation":[67,71],"classical":[69],"local":[70],"studied":[73],"within":[74],"continuous":[75],"space.":[78],"Numerical":[79],"experiments":[80],"(1D)":[81],"also":[83],"given":[84],"test":[86],"theoretical":[88],"conclusions.":[89]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":13},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
