{"id":"https://openalex.org/W2058053161","doi":"https://doi.org/10.1137/030602745","title":"Convergence of Upwind Finite Difference Schemes for a Scalar Conservation Law with Indefinite Discontinuities in the Flux Function","display_name":"Convergence of Upwind Finite Difference Schemes for a Scalar Conservation Law with Indefinite Discontinuities in the Flux Function","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2058053161","doi":"https://doi.org/10.1137/030602745","mag":"2058053161"},"language":"en","primary_location":{"id":"doi:10.1137/030602745","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030602745","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/A5101961582","display_name":"Siddhartha Mishra","orcid":"https://orcid.org/0000-0002-2665-5385"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Siddhartha Mishra","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5101961582"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.0031,"has_fulltext":false,"cited_by_count":42,"citation_normalized_percentile":{"value":0.97776516,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"43","issue":"2","first_page":"559","last_page":"577"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9991000294685364,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9991000294685364,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9952999949455261,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9908000230789185,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7853412628173828},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.7746699452400208},{"id":"https://openalex.org/keywords/heaviside-step-function","display_name":"Heaviside step function","score":0.7022773027420044},{"id":"https://openalex.org/keywords/godunovs-scheme","display_name":"Godunov's scheme","score":0.6810364723205566},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6540955305099487},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.5999482870101929},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5817159414291382},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.548524022102356},{"id":"https://openalex.org/keywords/riemann-problem","display_name":"Riemann problem","score":0.4839073121547699},{"id":"https://openalex.org/keywords/weak-solution","display_name":"Weak solution","score":0.4481132924556732},{"id":"https://openalex.org/keywords/upwind-scheme","display_name":"Upwind scheme","score":0.4351266622543335},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.43488407135009766},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.42116817831993103},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3585164546966553},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.32819104194641113},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.2622930407524109},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21109789609909058}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7853412628173828},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.7746699452400208},{"id":"https://openalex.org/C7980502","wikidata":"https://www.wikidata.org/wiki/Q322339","display_name":"Heaviside step function","level":2,"score":0.7022773027420044},{"id":"https://openalex.org/C146705398","wikidata":"https://www.wikidata.org/wiki/Q4291826","display_name":"Godunov's scheme","level":3,"score":0.6810364723205566},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6540955305099487},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.5999482870101929},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5817159414291382},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.548524022102356},{"id":"https://openalex.org/C40709475","wikidata":"https://www.wikidata.org/wiki/Q2152221","display_name":"Riemann problem","level":3,"score":0.4839073121547699},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.4481132924556732},{"id":"https://openalex.org/C94025248","wikidata":"https://www.wikidata.org/wiki/Q7899499","display_name":"Upwind scheme","level":3,"score":0.4351266622543335},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.43488407135009766},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42116817831993103},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3585164546966553},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.32819104194641113},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2622930407524109},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21109789609909058},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/030602745","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030602745","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:eprints.iisc.ac.in:15157","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196309","display_name":"NOT FOUND REPOSITORY (Indian Institute of Science Bangalore)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I59270414","host_organization_name":"Indian Institute of Science Bangalore","host_organization_lineage":["https://openalex.org/I59270414"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.6200000047683716}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1544776024","https://openalex.org/W1972076817","https://openalex.org/W1972578258","https://openalex.org/W1977839485","https://openalex.org/W1992812527","https://openalex.org/W1996934806","https://openalex.org/W1998407280","https://openalex.org/W1998483100","https://openalex.org/W2038327721","https://openalex.org/W2038831503","https://openalex.org/W2045679525","https://openalex.org/W2055064622","https://openalex.org/W2062142591","https://openalex.org/W2070133075","https://openalex.org/W2072472676","https://openalex.org/W2090484913","https://openalex.org/W2091656256","https://openalex.org/W2099854605","https://openalex.org/W2128497465","https://openalex.org/W2130212979","https://openalex.org/W2472436849","https://openalex.org/W2481459718"],"related_works":["https://openalex.org/W4295135832","https://openalex.org/W2520772736","https://openalex.org/W4240076417","https://openalex.org/W2267387804","https://openalex.org/W2350290936","https://openalex.org/W1977614220","https://openalex.org/W3035499973","https://openalex.org/W2371649168","https://openalex.org/W1980014272","https://openalex.org/W2142612945"],"abstract_inverted_index":{"We":[0,104],"consider":[1],"the":[2,11,41,51,110,116,137,140,159,168,172,178],"scalar":[3,180],"conservation":[4,181],"law":[5,182],"with":[6,50,167,183,206],"flux":[7,173],"function":[8,43],"discontinuous":[9,184],"in":[10],"space":[12],"variable,":[13],"i.e.,":[14],"\\begin{eqnarray}":[15],"\\label{eq1}":[16],"u_t+(H(x)f(u)+(1-H(x))g(u))_{x}":[17],"&=&":[18,30],"0":[19],"\\quad":[20,32],"\\mbox{in":[21,33],"}":[22,34],"\\R":[23],"\\times":[24],"\\R_{+},":[25],"\\nonumber":[26],"\\\\":[27,197],"u(0,":[28],"x)":[29,200],"u_{0}(x)":[31],"\\R,":[35],"\\label{0.1}":[36],"\\end{eqnarray}":[37],"where":[38],"H":[39],"is":[40,56,60,64,68,78,136],"Heaviside":[42],"and":[44,46,58,66,89,127,209],"f":[45,55,63,193,207],"g":[47,59,67],"are":[48],"smooth":[49],"assumptions":[52],"that":[53,82,158],"either":[54],"convex":[57,208],"concave":[61,65],"or":[62],"convex.":[69],"The":[70,130],"existence":[71],"of":[72,76,87,118,125,133,139,151,164,211],"a":[73,94,100],"weak":[74,95],"solution":[75],"(\\ref{eq1})":[77,166],"proved":[79],"by":[80],"showing":[81],"upwind":[83],"finite":[84],"difference":[85],"schemes":[86,124,161],"Godunov":[88,126],"Enquist--Osher":[90,128],"type":[91,165],"converge":[92],"to":[93,109,156],"solution.":[96],"Uniqueness":[97],"follows":[98],"from":[99],"Kruzkhov-type":[101],"entropy":[102],"condition.":[103],"also":[105],"provide":[106],"explicit":[107],"solutions":[108],"Riemann":[111],"problem":[112],"for":[113,148],"(\\ref{eq1}).":[114],"At":[115],"level":[117],"numerics,":[119],"we":[120],"give":[121],"easy-to-implement":[122],"numerical":[123,160],"type.":[129],"central":[131],"feature":[132],"this":[134],"paper":[135],"modification":[138],"singular":[141],"mapping":[142],"technique":[143],"(the":[144],"main":[145],"analytical":[146],"tool":[147],"these":[149],"types":[150],"equations)":[152],"which":[153],"allows":[154],"us":[155],"show":[157],"converge.":[162],"Equations":[163],"above":[169],"hypothesis":[170],"on":[171],"may":[174],"occur":[175],"when":[176],"considering":[177],"following":[179],"flux:":[185],"\\begin{equation}":[186],"\\label{eq2}":[187],"\\begin{array}{r@{\\;}l}":[188],"u_t":[189],"+":[190],"(k":[191],"(x)":[192],"(u))_x":[194],"&=":[195,201],"0,":[196],"u":[198],"(0,":[199],"u_0":[202],"(x),":[203],"\\end{array}":[204],"\\end{equation}":[205],"k":[210],"indefinite":[212],"sign.":[213]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-25T06:16:34.145877","created_date":"2025-10-10T00:00:00"}
