{"id":"https://openalex.org/W2165807641","doi":"https://doi.org/10.1137/040612099","title":"Some new error estimates of a semidiscrete finite volume element method for a parabolic integro-differential equation with nonsmooth initial data","display_name":"Some new error estimates of a semidiscrete finite volume element method for a parabolic integro-differential equation with nonsmooth initial data","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2165807641","doi":"https://doi.org/10.1137/040612099","mag":"2165807641"},"language":"en","primary_location":{"id":"doi:10.1137/040612099","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040612099","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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/A5019723508","display_name":"Rajen Kumar Sinha","orcid":"https://orcid.org/0000-0002-5910-8943"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rajen K. Sinha","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112526925","display_name":"Richard E. Ewing","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Richard E. Ewing","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5077310702","display_name":"Raytcho Lazarov","orcid":"https://orcid.org/0000-0002-4911-3685"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Raytcho D. Lazarov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6997,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.848719,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"43","issue":"6","first_page":"2320","last_page":"2343"},"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":0.9994999766349792,"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":0.9994999766349792,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9988999962806702,"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/mathematics","display_name":"Mathematics","score":0.8692531585693359},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5815233588218689},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5657232999801636},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5123151540756226},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4967361092567444},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.49069225788116455},{"id":"https://openalex.org/keywords/homogeneous-differential-equation","display_name":"Homogeneous differential equation","score":0.48241791129112244},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4328915476799011},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4214925169944763},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4190453588962555},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4105764925479889},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.14757055044174194},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08564865589141846}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8692531585693359},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5815233588218689},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5657232999801636},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5123151540756226},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4967361092567444},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.49069225788116455},{"id":"https://openalex.org/C22219631","wikidata":"https://www.wikidata.org/wiki/Q2434565","display_name":"Homogeneous differential equation","level":5,"score":0.48241791129112244},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4328915476799011},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4214925169944763},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4190453588962555},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4105764925479889},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.14757055044174194},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08564865589141846},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/040612099","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040612099","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.64.5455","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.64.5455","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.isc.tamu.edu/~ewing/pubs/318ewing2006.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.81.8783","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.81.8783","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.isc.tamu.edu/publications-reports/tr/0416.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.6800000071525574}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W69614788","https://openalex.org/W204801424","https://openalex.org/W1505377314","https://openalex.org/W1521920611","https://openalex.org/W1529316362","https://openalex.org/W1963952659","https://openalex.org/W1964925308","https://openalex.org/W1983486085","https://openalex.org/W1986267641","https://openalex.org/W1992025228","https://openalex.org/W1995151111","https://openalex.org/W2004967444","https://openalex.org/W2009477751","https://openalex.org/W2015221450","https://openalex.org/W2021510322","https://openalex.org/W2022591932","https://openalex.org/W2023963475","https://openalex.org/W2024050379","https://openalex.org/W2025944808","https://openalex.org/W2033672550","https://openalex.org/W2038281935","https://openalex.org/W2047162698","https://openalex.org/W2049571296","https://openalex.org/W2051831312","https://openalex.org/W2053385562","https://openalex.org/W2057046371","https://openalex.org/W2057646856","https://openalex.org/W2061478133","https://openalex.org/W2061991768","https://openalex.org/W2076642757","https://openalex.org/W2082621526","https://openalex.org/W2089766265","https://openalex.org/W2121410213","https://openalex.org/W4242273588","https://openalex.org/W4247711213"],"related_works":["https://openalex.org/W2347435260","https://openalex.org/W2382658150","https://openalex.org/W2348403575","https://openalex.org/W2419155800","https://openalex.org/W2359059858","https://openalex.org/W2379168511","https://openalex.org/W1991622226","https://openalex.org/W2361682731","https://openalex.org/W2353151757","https://openalex.org/W3179404742"],"abstract_inverted_index":{"A":[0],"semidiscrete":[1],"finite":[2],"volume":[3],"element":[4],"(FVE)":[5],"approximation":[6],"to":[7,57],"a":[8,16,52],"parabolic":[9],"integro-differential":[10],"equation":[11],"(PIDE)":[12],"is":[13,77],"analyzed":[14],"in":[15,66,79],"two-dimensional":[17],"convex":[18],"polygonal":[19],"domain.":[20],"An":[21],"optimal-order":[22,33],"$L^2$-error":[23,34],"estimate":[24,35,61],"for":[25,36,44,69],"smooth":[26],"initial":[27,38,75],"data":[28,39],"and":[29,51],"nearly":[30],"the":[31,67,73],"same":[32],"nonsmooth":[37],"are":[40,55],"obtained.":[41],"More":[42],"precisely,":[43],"homogeneous":[45],"equations,":[46],"an":[47,59],"elementary":[48],"energy":[49],"technique":[50],"duality":[53],"argument":[54],"used":[56],"derive":[58],"error":[60],"of":[62],"order":[63],"$O\\left(t^{-1}{h^2}\\ln":[64],"h\\right)$":[65],"$L^2$-norm":[68],"positive":[70],"time":[71],"when":[72],"given":[74],"function":[76],"only":[78],"$L^2$.":[80]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}