{"id":"https://openalex.org/W2055880686","doi":"https://doi.org/10.1137/140965326","title":"High Order Maximum-Principle-Preserving Discontinuous Galerkin Method for Convection-Diffusion Equations","display_name":"High Order Maximum-Principle-Preserving Discontinuous Galerkin Method for Convection-Diffusion Equations","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2055880686","doi":"https://doi.org/10.1137/140965326","mag":"2055880686"},"language":"en","primary_location":{"id":"doi:10.1137/140965326","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140965326","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/A5012141054","display_name":"Tao Xiong","orcid":"https://orcid.org/0000-0002-4912-6574"},"institutions":[{"id":"https://openalex.org/I44461941","display_name":"University of Houston","ror":"https://ror.org/048sx0r50","country_code":"US","type":"education","lineage":["https://openalex.org/I44461941"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tao Xiong","raw_affiliation_strings":["[Univ. of Houston]"],"affiliations":[{"raw_affiliation_string":"[Univ. of Houston]","institution_ids":["https://openalex.org/I44461941"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065678545","display_name":"Jing\u2010Mei Qiu","orcid":"https://orcid.org/0000-0002-4226-6080"},"institutions":[{"id":"https://openalex.org/I44461941","display_name":"University of Houston","ror":"https://ror.org/048sx0r50","country_code":"US","type":"education","lineage":["https://openalex.org/I44461941"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jing-Mei Qiu","raw_affiliation_strings":["[Univ. of Houston]"],"affiliations":[{"raw_affiliation_string":"[Univ. of Houston]","institution_ids":["https://openalex.org/I44461941"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101993671","display_name":"Zhengfu Xu","orcid":"https://orcid.org/0000-0003-1482-5727"},"institutions":[{"id":"https://openalex.org/I11957088","display_name":"Michigan Technological University","ror":"https://ror.org/0036rpn28","country_code":"US","type":"education","lineage":["https://openalex.org/I11957088"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhengfu Xu","raw_affiliation_strings":[", Michigan Technological University"],"affiliations":[{"raw_affiliation_string":", Michigan Technological University","institution_ids":["https://openalex.org/I11957088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5012141054"],"corresponding_institution_ids":["https://openalex.org/I44461941"],"apc_list":null,"apc_paid":null,"fwci":3.6883,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.92343317,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"37","issue":"2","first_page":"A583","last_page":"A608"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","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/T11416","display_name":"Numerical methods for differential equations","score":0.9987999796867371,"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/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7794499397277832},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7577383518218994},{"id":"https://openalex.org/keywords/flux-limiter","display_name":"Flux limiter","score":0.7449275255203247},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.5511149168014526},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5502609014511108},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5161920189857483},{"id":"https://openalex.org/keywords/limiter","display_name":"Limiter","score":0.49396830797195435},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.455637127161026},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.4338812232017517},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43305450677871704},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.25314146280288696},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19259628653526306},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16115552186965942},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11172345280647278}],"concepts":[{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7794499397277832},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7577383518218994},{"id":"https://openalex.org/C10819784","wikidata":"https://www.wikidata.org/wiki/Q5463027","display_name":"Flux limiter","level":2,"score":0.7449275255203247},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.5511149168014526},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5502609014511108},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5161920189857483},{"id":"https://openalex.org/C45011657","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiter","level":2,"score":0.49396830797195435},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.455637127161026},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4338812232017517},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43305450677871704},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.25314146280288696},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19259628653526306},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16115552186965942},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11172345280647278},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/140965326","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140965326","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:digitalcommons.mtu.edu:michigantech-p-31634","is_oa":false,"landing_page_url":"https://digitalcommons.mtu.edu/michigantech-p/12332","pdf_url":null,"source":{"id":"https://openalex.org/S4377196391","display_name":"Digital Commons - Michigan Tech (Michigan Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I11957088","host_organization_name":"Michigan Technological University","host_organization_lineage":["https://openalex.org/I11957088"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Michigan Tech Publications, Part 1","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2358482728","display_name":"High Order Maximum Principle Preserving Finite Difference Schemes for Hyperbolic Conservation Laws","funder_award_id":"1316662","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2537814734","display_name":null,"funder_award_id":"DMS-1316662","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6580533321","display_name":null,"funder_award_id":"DMS-1217008","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6848654469","display_name":"A High Order Semi-Lagrangian Approach for the Vlasov Equation","funder_award_id":"1217008","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W70071832","https://openalex.org/W157107253","https://openalex.org/W1507767947","https://openalex.org/W1555627060","https://openalex.org/W1600997507","https://openalex.org/W1886421468","https://openalex.org/W1963487408","https://openalex.org/W1967467186","https://openalex.org/W1969395389","https://openalex.org/W1973481688","https://openalex.org/W1982465309","https://openalex.org/W1983195644","https://openalex.org/W1988507032","https://openalex.org/W1989692168","https://openalex.org/W1993923624","https://openalex.org/W2008956940","https://openalex.org/W2012541063","https://openalex.org/W2012938047","https://openalex.org/W2019713093","https://openalex.org/W2029957540","https://openalex.org/W2038007684","https://openalex.org/W2039150507","https://openalex.org/W2051370422","https://openalex.org/W2054597080","https://openalex.org/W2058765828","https://openalex.org/W2063214641","https://openalex.org/W2065908448","https://openalex.org/W2072099237","https://openalex.org/W2085961649","https://openalex.org/W2092584883","https://openalex.org/W2111377397","https://openalex.org/W2142212336","https://openalex.org/W2156669471","https://openalex.org/W2953260897","https://openalex.org/W4252060206","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1994462981","https://openalex.org/W4286962991","https://openalex.org/W2941134316","https://openalex.org/W3027009359","https://openalex.org/W3202315186","https://openalex.org/W4389166462","https://openalex.org/W2374241667","https://openalex.org/W1998416284","https://openalex.org/W2381269531","https://openalex.org/W2073662629"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,100],"propose":[4],"to":[5,28,142,154,170],"apply":[6],"the":[7,29,36,43,51,57,72,77,102,116,155,173,183,204,209,213,216],"parametrized":[8,135],"maximum-principle-preserving":[9],"(MPP)":[10],"flux":[11,46,68,137,176],"limiter":[12,138,177],"in":[13,62,75,115],"[T.":[14],"Xiong,":[15],"J.-M.":[16],"Qiu,":[17],"and":[18,90,212],"Z.":[19],"Xu,":[20],"J.":[21,93],"Comput.":[22,94],"Phys.,":[23,95],"252":[24],"(2013),":[25],"pp.":[26,98],"310--331]":[27],"discontinuous":[30],"Galerkin":[31],"(DG)":[32],"method":[33,178],"for":[34,83,121,162,199],"solving":[35],"convection-diffusion":[37,84],"equations.":[38],"The":[39],"feasibility":[40],"of":[41,56,80,104,112,118,124,145,215],"applying":[42],"proposed":[44,134,174,217],"MPP":[45,78,136,175,210],"limiters":[47],"is":[48,168],"based":[49],"on":[50],"fact":[52],"that":[53,152,172],"cell":[54,106],"averages":[55,107],"DG":[58,81,122,143],"solutions":[59,82],"are":[60],"updated":[61],"a":[63,109,131],"conservative":[64],"fashion":[65],"(by":[66],"using":[67],"difference).":[69],"Compared":[70],"with":[71],"earlier":[73],"approach":[74],"preserving":[76],"property":[79],"problems":[85],"[Y.":[86],"Zhang,":[87,89],"X.":[88],"C.-W.":[91],"Shu,":[92],"234":[96],"(2012),":[97],"295--316],":[99],"avoid":[101],"difficulty":[103],"rewriting":[105],"as":[108],"convex":[110],"combination":[111],"point":[113],"values":[114],"presence":[117],"diffusion":[119],"terms":[120],"schemes":[123],"higher":[125],"than":[126],"second":[127],"order":[128,157,186,206],"accuracy.":[129],"As":[130],"result,":[132],"our":[133],"can":[139,159],"be":[140,160],"applied":[141],"methods":[144],"arbitrary":[146],"high":[147,185,205],"order.":[148],"We":[149],"theoretically":[150],"prove":[151],"up":[153],"third":[156],"accuracy":[158,207],"preserved":[161],"scalar":[163],"one-dimensional":[164],"problems.":[165],"Numerical":[166,195],"evidence":[167],"presented":[169],"show":[171],"does":[179,189],"not":[180],"adversely":[181],"affect":[182],"desired":[184],"accuracy,":[187],"nor":[188],"it":[190],"require":[191],"restrictive":[192],"time":[193],"steps.":[194],"experiments":[196],"including":[197],"those":[198],"incompressible":[200],"flow":[201],"examples":[202],"demonstrate":[203],"preserving,":[208],"performance,":[211],"robustness":[214],"method.":[218]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
