{"id":"https://openalex.org/W2121296933","doi":"https://doi.org/10.1137/s1064827501389084","title":"Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws","display_name":"Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2121296933","doi":"https://doi.org/10.1137/s1064827501389084","mag":"2121296933"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827501389084","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827501389084","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5068101054","display_name":"Ralf Hartmann","orcid":"https://orcid.org/0000-0002-0403-1221"},"institutions":[{"id":"https://openalex.org/I223822909","display_name":"Heidelberg University","ror":"https://ror.org/038t36y30","country_code":"DE","type":"education","lineage":["https://openalex.org/I223822909"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ralf Hartmann","raw_affiliation_strings":["Heidelberg University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Heidelberg University","institution_ids":["https://openalex.org/I223822909"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035584552","display_name":"Paul Houston","orcid":"https://orcid.org/0000-0002-3588-2029"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Paul Houston","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":12.3542,"has_fulltext":false,"cited_by_count":159,"citation_normalized_percentile":{"value":0.99114844,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"24","issue":"3","first_page":"979","last_page":"1004"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9997000098228455,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9997000098228455,"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/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/T11416","display_name":"Numerical methods for differential equations","score":0.9918000102043152,"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":0.7645199298858643},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6633734107017517},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.6546161770820618},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.5807746648788452},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5737229585647583},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5438629984855652},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5371891260147095},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.522377073764801},{"id":"https://openalex.org/keywords/adaptive-mesh-refinement","display_name":"Adaptive mesh refinement","score":0.46280211210250854},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.42803633213043213},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.4267881512641907},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3882981538772583},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2910745441913605},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12547898292541504}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7645199298858643},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6633734107017517},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.6546161770820618},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.5807746648788452},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5737229585647583},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5438629984855652},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5371891260147095},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.522377073764801},{"id":"https://openalex.org/C131053463","wikidata":"https://www.wikidata.org/wiki/Q4680751","display_name":"Adaptive mesh refinement","level":2,"score":0.46280211210250854},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.42803633213043213},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.4267881512641907},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3882981538772583},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2910745441913605},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12547898292541504},{"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/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s1064827501389084","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827501389084","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7099999785423279,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W68408985","https://openalex.org/W1535260321","https://openalex.org/W1537224157","https://openalex.org/W1537551582","https://openalex.org/W1595775464","https://openalex.org/W1600997507","https://openalex.org/W1979413834","https://openalex.org/W2010271936","https://openalex.org/W2037850364","https://openalex.org/W2041232459","https://openalex.org/W2044653767","https://openalex.org/W2047554497","https://openalex.org/W2052434397","https://openalex.org/W2054873122","https://openalex.org/W2059017100","https://openalex.org/W2069930283","https://openalex.org/W2070533863","https://openalex.org/W2085961649","https://openalex.org/W2086654907","https://openalex.org/W2104102694","https://openalex.org/W2118341834","https://openalex.org/W2148639620","https://openalex.org/W2476121372","https://openalex.org/W2525823748","https://openalex.org/W3046101478","https://openalex.org/W4206139584","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2726528067","https://openalex.org/W2129573473","https://openalex.org/W2053583759","https://openalex.org/W2380255313","https://openalex.org/W2952149072","https://openalex.org/W2120874885","https://openalex.org/W2154700905","https://openalex.org/W2138882090","https://openalex.org/W4366777355","https://openalex.org/W2162026849"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,28,38,43,54,87,90,99,115,134,138,148,153,156,176],"a":[3,60,69,79,102,160,167],"posteriori":[4,80,161],"error":[5,31,81,84,162,190],"analysis":[6],"and":[7,48,56,123,152],"adaptive":[8,126,150],"mesh":[9,183],"design":[10,122],"for":[11,33],"discontinuous":[12],"Galerkin":[13],"finite":[14,91],"element":[15,92],"approximations":[16],"to":[17,133],"systems":[18],"of":[19,30,37,59,89,101,137,142,147,155,169,178],"nonlinear":[20],"hyperbolic":[21],"conservation":[22],"laws.":[23],"In":[24,172],"particular,":[25,173],"we":[26,72,121,174],"discuss":[27],"question":[29],"estimation":[32],"general":[34],"target":[35,140],"functionals":[36],"solution;":[39],"typical":[40],"examples":[41],"include":[42,86],"outflow":[44],"flux,":[45],"local":[46,95],"average":[47],"pointwise":[49],"value,":[50],"as":[51,53],"well":[52],"lift":[55],"drag":[57],"coefficients":[58],"body":[61],"immersed":[62],"in":[63],"an":[64,125],"inviscid":[65],"fluid.":[66],"By":[67],"employing":[68],"duality":[70],"argument,":[71],"derive":[73],"so-called":[74],"weighted":[75],"or":[76,105],"Type":[77,118,158,188],"I":[78,119,159],"bounds;":[82],"these":[83],"estimates":[85],"product":[88],"residuals":[93],"with":[94],"weighting":[96],"terms":[97],"involving":[98],"solution":[100],"certain":[103],"dual":[104],"adjoint":[106],"problem":[107],"that":[108,128],"must":[109],"be":[110],"numerically":[111],"approximated.":[112],"Based":[113],"on":[114],"resulting":[116],"approximate":[117,157],"bound,":[120],"implement":[124],"algorithm":[127],"produces":[129],"meshes":[130],"specifically":[131],"tailored":[132],"efficient":[135],"computation":[136],"given":[139],"functional":[141],"practical":[143],"interest.":[144],"The":[145],"performance":[146],"proposed":[149],"strategy":[151],"quality":[154],"bound":[163],"is":[164],"illustrated":[165],"by":[166],"series":[168],"numerical":[170],"experiments.":[171],"demonstrate":[175],"superiority":[177],"this":[179],"approach":[180],"over":[181],"standard":[182],"refinement":[184],"algorithms":[185],"which":[186],"employ":[187],"II":[189],"indicators.":[191]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
