{"id":"https://openalex.org/W1986006981","doi":"https://doi.org/10.1137/040619314","title":"hp-Discontinuous Galerkin Time-Stepping for Volterra Integrodifferential Equations","display_name":"hp-Discontinuous Galerkin Time-Stepping for Volterra Integrodifferential Equations","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1986006981","doi":"https://doi.org/10.1137/040619314","mag":"1986006981"},"language":"en","primary_location":{"id":"doi:10.1137/040619314","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040619314","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/A5031788253","display_name":"Hermann Brunner","orcid":"https://orcid.org/0000-0002-0089-3481"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hermann Brunner","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5000032948","display_name":"Dominik Sch\u00f6tzau","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dominik Sch\u00f6tzau","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5031788253"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1174,"has_fulltext":false,"cited_by_count":77,"citation_normalized_percentile":{"value":0.85558653,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"44","issue":"1","first_page":"224","last_page":"245"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9997000098228455,"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":0.8714948892593384},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.670066237449646},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.6595962047576904},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.596731960773468},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5695347189903259},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.561863362789154},{"id":"https://openalex.org/keywords/time-stepping","display_name":"Time stepping","score":0.5439327955245972},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5338621735572815},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5060479044914246},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5013716220855713},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.48748779296875},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.48711180686950684},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.2116619348526001},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.21028205752372742},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1339598298072815},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.08780971169471741}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8714948892593384},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.670066237449646},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.6595962047576904},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.596731960773468},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5695347189903259},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.561863362789154},{"id":"https://openalex.org/C3019693144","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Time stepping","level":3,"score":0.5439327955245972},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5338621735572815},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5060479044914246},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5013716220855713},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.48748779296875},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.48711180686950684},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.2116619348526001},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.21028205752372742},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1339598298072815},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.08780971169471741},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/040619314","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040619314","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W202835528","https://openalex.org/W1567668233","https://openalex.org/W1966192083","https://openalex.org/W1967203400","https://openalex.org/W1979762896","https://openalex.org/W1984257336","https://openalex.org/W1986683394","https://openalex.org/W2062326781","https://openalex.org/W2063164826","https://openalex.org/W2073689707","https://openalex.org/W2081416965","https://openalex.org/W2088789193","https://openalex.org/W2089181747","https://openalex.org/W2090886631","https://openalex.org/W4242273588","https://openalex.org/W4247874407"],"related_works":["https://openalex.org/W2335200596","https://openalex.org/W2162026849","https://openalex.org/W1991867815","https://openalex.org/W2394687667","https://openalex.org/W2133369474","https://openalex.org/W2524024922","https://openalex.org/W2899284167","https://openalex.org/W1967203400","https://openalex.org/W2924897202","https://openalex.org/W1994841366"],"abstract_inverted_index":{"We":[0,19],"present":[1],"an":[2],"hp-error":[3],"analysis":[4],"of":[5,32,40,57,72],"the":[6,28,30,33,37,41],"discontinuous":[7],"Galerkin":[8],"time-stepping":[9],"method":[10],"for":[11],"Volterra":[12],"integrodifferential":[13],"equations":[14],"with":[15],"weakly":[16],"singular":[17],"kernels.":[18],"derive":[20],"new":[21],"error":[22],"bounds":[23],"that":[24,48],"are":[25,67],"explicit":[26],"in":[27,69],"time-steps,":[29],"degrees":[31],"approximating":[34],"polynomials,":[35],"and":[36],"regularity":[38],"properties":[39],"exact":[42],"solution.":[43],"It":[44],"is":[45],"then":[46],"shown":[47],"start-up":[49],"singularities":[50],"can":[51],"be":[52],"resolved":[53],"at":[54],"exponential":[55],"rates":[56],"convergence":[58],"by":[59],"using":[60],"geometrically":[61],"graded":[62],"time-steps.":[63],"Our":[64],"theoretical":[65],"results":[66],"confirmed":[68],"a":[70],"series":[71],"numerical":[73],"tests.":[74]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-30T08:08:38.191290","created_date":"2025-10-10T00:00:00"}
