{"id":"https://openalex.org/W2008531454","doi":"https://doi.org/10.1137/120898620","title":"Convergence Analysis of a Discontinuous Galerkin/Strang Splitting Approximation for the Vlasov--Poisson Equations","display_name":"Convergence Analysis of a Discontinuous Galerkin/Strang Splitting Approximation for the Vlasov--Poisson Equations","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2008531454","doi":"https://doi.org/10.1137/120898620","mag":"2008531454"},"language":"en","primary_location":{"id":"doi:10.1137/120898620","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120898620","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1211.2353","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Lukas Einkemmer","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lukas Einkemmer","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Alexander Ostermann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexander Ostermann","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7372,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.92281202,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"52","issue":"2","first_page":"757","last_page":"778"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.6875,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.6875,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.15360000729560852,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.050200000405311584,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7455000281333923},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7008000016212463},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6243000030517578},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5327000021934509},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.5198000073432922},{"id":"https://openalex.org/keywords/numerical-approximation","display_name":"Numerical approximation","score":0.45579999685287476},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.43950000405311584},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4375999867916107},{"id":"https://openalex.org/keywords/order-of-accuracy","display_name":"Order of accuracy","score":0.424699991941452}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8580999970436096},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7455000281333923},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7008000016212463},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6243000030517578},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5327000021934509},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5271000266075134},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.5198000073432922},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4578999876976013},{"id":"https://openalex.org/C2986878899","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical approximation","level":3,"score":0.45579999685287476},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.43950000405311584},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4375999867916107},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.424699991941452},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.4083999991416931},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4049000144004822},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.34369999170303345},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.3303999900817871},{"id":"https://openalex.org/C89397928","wikidata":"https://www.wikidata.org/wiki/Q1630320","display_name":"Unconditional convergence","level":5,"score":0.32589998841285706},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.28610000014305115},{"id":"https://openalex.org/C2987355758","wikidata":"https://www.wikidata.org/wiki/Q25037251","display_name":"Operator splitting","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.25540000200271606},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/120898620","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120898620","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:arXiv.org:1211.2353","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1211.2353","pdf_url":"https://arxiv.org/pdf/1211.2353","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1211.2353","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1211.2353","pdf_url":"https://arxiv.org/pdf/1211.2353","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1592378316","https://openalex.org/W1953185199","https://openalex.org/W1963526434","https://openalex.org/W1973071367","https://openalex.org/W1974099477","https://openalex.org/W1978443201","https://openalex.org/W1980011357","https://openalex.org/W1988732325","https://openalex.org/W1994615527","https://openalex.org/W2022509807","https://openalex.org/W2026836732","https://openalex.org/W2043376739","https://openalex.org/W2056413133","https://openalex.org/W2060331029","https://openalex.org/W2060908471","https://openalex.org/W2086617698","https://openalex.org/W2088015249","https://openalex.org/W2090446569"],"related_works":[],"abstract_inverted_index":{"A":[0],"rigorous":[1],"convergence":[2],"analysis":[3],"of":[4,32,41,54,68,88],"the":[5,17,29,39,47,52,55,63,76,84],"Strang":[6],"splitting":[7],"algorithm":[8,77],"with":[9,78],"a":[10,42,86],"discontinuous":[11,56],"Galerkin":[12,57],"approximation":[13],"in":[14,83],"space":[15],"for":[16,66],"Vlasov--Poisson":[18],"equations":[19],"is":[20,23,31,38,46],"provided.":[21],"It":[22],"shown":[24],"that":[25],"under":[26],"suitable":[27],"assumptions":[28],"error":[30],"order":[33,53,60,70],"$\\mathcal{O}(\\tau^2+h^q":[34],"+h^q/\\tau)$,":[35],"where":[36],"$\\tau$":[37],"size":[40],"time":[43],"step,":[44],"$h$":[45],"cell":[48],"size,":[49],"and":[50],"$q$":[51],"approximation.":[58],"In":[59],"to":[61,74],"investigate":[62],"recurrence":[64],"phenomena":[65],"approximations":[67],"higher":[69],"as":[71,73],"well":[72],"compare":[75],"numerical":[79,89],"results":[80],"already":[81],"available":[82],"literature":[85],"number":[87],"simulations":[90],"are":[91],"performed.":[92]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":3}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2016-06-24T00:00:00"}