{"id":"https://openalex.org/W2586347246","doi":"https://doi.org/10.1515/jnma-2016-1056","title":"Error estimates for higher-order finite volume schemes for convection\u2013diffusion problems","display_name":"Error estimates for higher-order finite volume schemes for convection\u2013diffusion problems","publication_year":2017,"publication_date":"2017-02-05","ids":{"openalex":"https://openalex.org/W2586347246","doi":"https://doi.org/10.1515/jnma-2016-1056","mag":"2586347246"},"language":"en","primary_location":{"id":"doi:10.1515/jnma-2016-1056","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnma-2016-1056","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","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/A5112232900","display_name":"Dietmar Kr\u00f6ner","orcid":null},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Dietmar Kr\u00f6ner","raw_affiliation_strings":["Universit\u00e4t Freiburg, Institut f\u00fcr Angewandte Mathematik, Hermann-Herder-Str. 10, 79104, Freiburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Freiburg, Institut f\u00fcr Angewandte Mathematik, Hermann-Herder-Str. 10, 79104, Freiburg, Germany","institution_ids":["https://openalex.org/I161046081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033501522","display_name":"Mirko Rokyta","orcid":"https://orcid.org/0000-0002-1857-7460"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Mirko Rokyta","raw_affiliation_strings":["Charles University, Department of Mathematical Analysis, Sokolovsk\u00e1 83, 186 75, Praha, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Charles University, Department of Mathematical Analysis, Sokolovsk\u00e1 83, 186 75, Praha, Czech Republic","institution_ids":["https://openalex.org/I21250087"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5033501522"],"corresponding_institution_ids":["https://openalex.org/I21250087"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.01604401,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"26","issue":"1","first_page":"35","last_page":"62"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9991000294685364,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.989799976348877,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/flux-limiter","display_name":"Flux limiter","score":0.7712026834487915},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7596282362937927},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7485560774803162},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.728071928024292},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6909264326095581},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5917699933052063},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.5701219439506531},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5579556226730347},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5489158034324646},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.5108177661895752},{"id":"https://openalex.org/keywords/convection","display_name":"Convection","score":0.41243425011634827},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3182918429374695},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15847906470298767},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.0859270989894867}],"concepts":[{"id":"https://openalex.org/C10819784","wikidata":"https://www.wikidata.org/wiki/Q5463027","display_name":"Flux limiter","level":2,"score":0.7712026834487915},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7596282362937927},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7485560774803162},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.728071928024292},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6909264326095581},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5917699933052063},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.5701219439506531},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5579556226730347},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5489158034324646},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.5108177661895752},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.41243425011634827},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3182918429374695},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15847906470298767},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0859270989894867},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/jnma-2016-1056","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnma-2016-1056","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","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":48,"referenced_works":["https://openalex.org/W140909251","https://openalex.org/W1537551582","https://openalex.org/W1570781527","https://openalex.org/W1580248330","https://openalex.org/W1593553932","https://openalex.org/W1889114201","https://openalex.org/W1964663237","https://openalex.org/W1970852400","https://openalex.org/W1972493351","https://openalex.org/W1978567204","https://openalex.org/W1982820457","https://openalex.org/W1982908458","https://openalex.org/W1989806103","https://openalex.org/W1993923624","https://openalex.org/W1994099903","https://openalex.org/W2000536171","https://openalex.org/W2005226957","https://openalex.org/W2008235068","https://openalex.org/W2011185352","https://openalex.org/W2018234142","https://openalex.org/W2022244525","https://openalex.org/W2031193793","https://openalex.org/W2033130775","https://openalex.org/W2039783631","https://openalex.org/W2041523977","https://openalex.org/W2045679525","https://openalex.org/W2051542828","https://openalex.org/W2060170348","https://openalex.org/W2065908448","https://openalex.org/W2067187920","https://openalex.org/W2079428675","https://openalex.org/W2080697504","https://openalex.org/W2091154395","https://openalex.org/W2093687887","https://openalex.org/W2094855393","https://openalex.org/W2107736107","https://openalex.org/W2120291421","https://openalex.org/W2147517700","https://openalex.org/W2152734519","https://openalex.org/W2255550747","https://openalex.org/W2286355715","https://openalex.org/W2341926591","https://openalex.org/W2469783257","https://openalex.org/W2479974775","https://openalex.org/W2491549679","https://openalex.org/W3020991820","https://openalex.org/W4240428608","https://openalex.org/W4247342202"],"related_works":["https://openalex.org/W2163017860","https://openalex.org/W2034255721","https://openalex.org/W828409841","https://openalex.org/W2384845972","https://openalex.org/W2090733834","https://openalex.org/W3091229350","https://openalex.org/W1977697942","https://openalex.org/W1984246786","https://openalex.org/W4213011511","https://openalex.org/W2979752376"],"abstract_inverted_index":{"Abstract":[0],"It":[1],"is":[2,98],"still":[3],"an":[4,69],"open":[5],"problem":[6,97,102],"to":[7,32,82,106],"prove":[8,65],"a":[9,54,70],"priori":[10,71],"error":[11,72],"estimates":[12],"for":[13,45],"finite":[14],"volume":[15],"schemes":[16,44],"of":[17,48,68,77,85],"higher":[18,42],"order":[19,34,43],"MUSCL":[20,107],"type,":[21],"including":[22],"limiters,":[23],"on":[24],"unstructured":[25],"meshes,":[26],"which":[27,80],"show":[28],"some":[29],"improvement":[30],"compared":[31],"first":[33],"schemes.":[35],"In":[36,74],"this":[37],"paper":[38],"we":[39,63,89],"use":[40],"these":[41],"the":[46,75,78,83,86,95,100],"discretization":[47,84],"convection":[49],"dominated":[50],"elliptic":[51],"problems":[52],"in":[53,59],"convex":[55],"bounded":[56],"domain":[57],"\u03a9":[58],"\u211d":[60],"2":[61],"and":[62],"can":[64],"such":[66],"kind":[67],"estimate.":[73],"part":[76],"estimate,":[79],"refers":[81],"convective":[87],"term,":[88],"gain":[90],"h":[91],"1/2":[92],".":[93],"Although":[94],"original":[96],"linear,":[99],"numerical":[101],"becomes":[103],"nonlinear,":[104],"due":[105],"type":[108],"reconstruction/limiter":[109],"technique.":[110]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}