{"id":"https://openalex.org/W2901277663","doi":"https://doi.org/10.1137/18m1227998","title":"Positivity Preserving Limiters for Time-Implicit Higher Order Accurate Discontinuous Galerkin Discretizations","display_name":"Positivity Preserving Limiters for Time-Implicit Higher Order Accurate Discontinuous Galerkin Discretizations","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2901277663","doi":"https://doi.org/10.1137/18m1227998","mag":"2901277663"},"language":"en","primary_location":{"id":"doi:10.1137/18m1227998","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1227998","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1811.08620","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030651554","display_name":"J.J.W. van der Vegt","orcid":"https://orcid.org/0000-0002-2690-0061"},"institutions":[{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"J. J. W. van der Vegt","raw_affiliation_strings":["Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500AE, Enschede, The Nether-lands"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500AE, Enschede, The Nether-lands","institution_ids":["https://openalex.org/I94624287"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035034346","display_name":"Yinhua Xia","orcid":"https://orcid.org/0000-0001-8120-3560"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yinhua Xia","raw_affiliation_strings":["School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078337531","display_name":"Yan Xu","orcid":"https://orcid.org/0000-0001-6483-4336"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yan Xu","raw_affiliation_strings":["Corresponding author. School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Corresponding author. School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5030651554"],"corresponding_institution_ids":["https://openalex.org/I94624287"],"apc_list":null,"apc_paid":null,"fwci":1.9409,"has_fulltext":true,"cited_by_count":40,"citation_normalized_percentile":{"value":0.84384025,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"41","issue":"3","first_page":"A2037","last_page":"A2063"},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9991000294685364,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9990000128746033,"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":0.832522988319397},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7646089792251587},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5933826565742493},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5851740837097168},{"id":"https://openalex.org/keywords/time-stepping","display_name":"Time stepping","score":0.4812778830528259},{"id":"https://openalex.org/keywords/limiter","display_name":"Limiter","score":0.4523346424102783},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.44672924280166626},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.44161728024482727},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37553513050079346},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.34341293573379517},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.3428708016872406},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13193097710609436}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.832522988319397},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7646089792251587},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5933826565742493},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5851740837097168},{"id":"https://openalex.org/C3019693144","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Time stepping","level":3,"score":0.4812778830528259},{"id":"https://openalex.org/C45011657","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiter","level":2,"score":0.4523346424102783},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.44672924280166626},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.44161728024482727},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37553513050079346},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.34341293573379517},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3428708016872406},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13193097710609436},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/18m1227998","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1227998","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"},{"id":"pmh:oai:arXiv.org:1811.08620","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.08620","pdf_url":"https://arxiv.org/pdf/1811.08620","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"},{"id":"pmh:oai:ris.utwente.nl:openaire_cris_publications/21a9c026-279f-4b51-9d49-6c4ccc088f7c","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/21a9c026-279f-4b51-9d49-6c4ccc088f7c","pdf_url":"https://ris.utwente.nl/ws/files/168414635/SISC_Vol41_3_ppA2037.pdf","source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"van der Vegt, J J W, Xia, Y & Xu, Y 2019, 'Positivity Preserving Limiters for Time-Implicit Higher Order Accurate Discontinuous Galerkin Discretizations', SIAM journal on scientific computing, vol. 41, no. 3, pp. A2037-A2063. https://doi.org/10.1137/18M1227998","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:ris.utwente.nl:publications/21a9c026-279f-4b51-9d49-6c4ccc088f7c","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1811.08620","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.08620","pdf_url":"https://arxiv.org/pdf/1811.08620","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":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.6399999856948853}],"awards":[{"id":"https://openalex.org/G241433331","display_name":null,"funder_award_id":"11871449","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G453636417","display_name":null,"funder_award_id":"11471306","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5939423041","display_name":null,"funder_award_id":"Technology","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7346218018","display_name":null,"funder_award_id":"11871","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7674826486","display_name":null,"funder_award_id":"11722112","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G79234895","display_name":null,"funder_award_id":"1172211","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7953310961","display_name":null,"funder_award_id":"91630207","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321015","display_name":"University of Twente","ror":"https://ror.org/006hf6230"},{"id":"https://openalex.org/F4320325599","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W321261355","https://openalex.org/W1486210902","https://openalex.org/W1543439990","https://openalex.org/W1551360398","https://openalex.org/W1579781026","https://openalex.org/W1592141884","https://openalex.org/W1968850685","https://openalex.org/W1972028349","https://openalex.org/W1973481688","https://openalex.org/W1992688650","https://openalex.org/W1994955324","https://openalex.org/W1995504856","https://openalex.org/W2008956940","https://openalex.org/W2009885647","https://openalex.org/W2012938047","https://openalex.org/W2014618205","https://openalex.org/W2038178878","https://openalex.org/W2051370422","https://openalex.org/W2059818040","https://openalex.org/W2073104520","https://openalex.org/W2076536542","https://openalex.org/W2076982741","https://openalex.org/W2078033075","https://openalex.org/W2091178963","https://openalex.org/W2096894484","https://openalex.org/W2120798238","https://openalex.org/W2124192278","https://openalex.org/W2156669471","https://openalex.org/W2166161964","https://openalex.org/W2218947347","https://openalex.org/W2244202970","https://openalex.org/W2274292815","https://openalex.org/W2318861708","https://openalex.org/W2530578203","https://openalex.org/W2744008313","https://openalex.org/W2766278830","https://openalex.org/W2782862523","https://openalex.org/W2964177232","https://openalex.org/W3010292040","https://openalex.org/W3084104286","https://openalex.org/W4301791716"],"related_works":["https://openalex.org/W4286962991","https://openalex.org/W2381269531","https://openalex.org/W2941134316","https://openalex.org/W1994462981","https://openalex.org/W2055696851","https://openalex.org/W3027009359","https://openalex.org/W2073662629","https://openalex.org/W3202315186","https://openalex.org/W4389166462","https://openalex.org/W1998416284"],"abstract_inverted_index":{"Currently,":[0],"nearly":[1],"all":[2],"positivity":[3,37,68,88,116,166,187,193],"preserving":[4,38,69,89,167,188,194],"discontinuous":[5],"Galerkin":[6],"(DG)":[7],"discretizations":[8,40],"of":[9,164,171,184],"partial":[10],"differential":[11],"equations":[12,135],"are":[13,71],"coupled":[14,73],"with":[15,46,79],"explicit":[16,36],"time":[17,48,84],"integration":[18,49,85],"methods.":[19,50],"Unfortunately,":[20],"for":[21,160,199],"many":[22],"problems":[23],"this":[24,52,172],"can":[25],"result":[26],"in":[27,104,113],"severe":[28],"time-step":[29],"restrictions.":[30],"The":[31,87,130,191],"techniques":[32],"used":[33],"to":[34,74,142],"develop":[35,149],"DG":[39,76,90,127,168,189,195],"cannot,":[41],"however,":[42,137],"easily":[43],"be":[44,118],"combined":[45,78],"implicit":[47,82],"In":[51],"paper,":[53],"we":[54],"therefore":[55,148],"present":[56],"a":[57,75,80,96,138,179],"new":[58],"approach.":[59],"Using":[60],"Lagrange":[61],"multipliers,":[62],"the":[63,67,108,124,161,185,207],"conditions":[64],"imposed":[65],"by":[66],"limiters":[70],"directly":[72],"discretization":[77,91,128,196],"diagonally":[81],"Runge--Kutta":[83],"method.":[86],"is":[92,101,110,158,176,197],"then":[93],"reformulated":[94],"as":[95],"Karush--Kuhn--Tucker":[97],"(KKT)":[98],"problem,":[99],"which":[100,205],"frequently":[102],"encountered":[103],"constrained":[105,144],"optimization.":[106],"Since":[107],"limiter":[109],"only":[111],"active":[112,152],"areas":[114],"where":[115],"must":[117],"enforced,":[119],"it":[120],"does":[121],"not":[122],"affect":[123],"higher":[125],"order":[126],"elsewhere.":[129],"resulting":[131],"nonsmooth":[132],"nonlinear":[133,201],"algebraic":[134],"have,":[136],"different":[139],"structure":[140],"compared":[141],"most":[143],"optimization":[145],"problems.":[146],"We":[147],"an":[150],"efficient":[151],"set":[153],"semismooth":[154,173],"Newton":[155,174],"method":[156,175],"that":[157],"suitable":[159],"KKT":[162],"formulation":[163],"time-implicit":[165,186,192],"discretizations.":[169],"Convergence":[170],"proven":[177],"using":[178],"specially":[180],"designed":[181],"quasi-directional":[182],"derivative":[183],"discretization.":[190],"demonstrated":[198],"several":[200],"scalar":[202],"conservation":[203],"laws,":[204],"include":[206],"advection,":[208],"Burgers,":[209],"Allen--Cahn,":[210],"Barenblatt,":[211],"and":[212],"Buckley--Leverett":[213],"equations.":[214]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2020-11-23T00:00:00"}
