{"id":"https://openalex.org/W2782043732","doi":"https://doi.org/10.1137/17m1152103","title":"A New HDG Method for Dirichlet Boundary Control of Convection Diffusion PDEs II: Low Regularity","display_name":"A New HDG Method for Dirichlet Boundary Control of Convection Diffusion PDEs II: Low Regularity","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2782043732","doi":"https://doi.org/10.1137/17m1152103","mag":"2782043732"},"language":"en","primary_location":{"id":"doi:10.1137/17m1152103","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1152103","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1801.01056","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Wei Gong","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wei Gong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Weiwei Hu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Weiwei Hu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Mariano Mateos","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mariano Mateos","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"John Singler","orcid":"https://orcid.org/0000-0002-5415-8386"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"John Singler","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5415-8386","affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Xiao Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiao Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Yangwen Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yangwen Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.491,"has_fulltext":true,"cited_by_count":25,"citation_normalized_percentile":{"value":0.87786596,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"56","issue":"4","first_page":"2262","last_page":"2287"},"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":0.9006999731063843,"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":0.9006999731063843,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.03790000081062317,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.022600000724196434,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"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":0.638700008392334},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6128000020980835},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5817000269889832},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5406000018119812},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.5121999979019165},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4896000027656555},{"id":"https://openalex.org/keywords/dirichlet-problem","display_name":"Dirichlet problem","score":0.48170000314712524},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.4562999904155731},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.4417000114917755}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.824400007724762},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.638700008392334},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6128000020980835},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5817000269889832},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5406000018119812},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5181000232696533},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.5121999979019165},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4896000027656555},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.48170000314712524},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46149998903274536},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.4562999904155731},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.4417000114917755},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.44029998779296875},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.43299999833106995},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.41130000352859497},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.3865000009536743},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3709999918937683},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.34290000796318054},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.33160001039505005},{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.3043000102043152},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.3027999997138977},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.27619999647140503},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2712000012397766},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.25540000200271606}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/17m1152103","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1152103","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:arXiv.org:1801.01056","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1801.01056","pdf_url":"https://arxiv.org/pdf/1801.01056","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:digibuo.uniovi.es:10651/49673","is_oa":false,"landing_page_url":"http://hdl.handle.net/10651/49673","pdf_url":null,"source":{"id":"https://openalex.org/S4306402334","display_name":"Consultation of the Doctoral Thesis Database (TESEO) (Ministerio de Educaci\u00f3n, Cultura y Deporte)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801976130","host_organization_name":"Ministerio de Educaci\u00f3n Cultura y Deporte","host_organization_lineage":["https://openalex.org/I2801976130"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1801.01056","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1801.01056","pdf_url":"https://arxiv.org/pdf/1801.01056","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":[],"awards":[{"id":"https://openalex.org/G2351394446","display_name":"Convergent Data-Based Algorithms for Model Reduction and Feedback Control of PDEs","funder_award_id":"1217122","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2373467387","display_name":"\u504f\u5fae\u5206\u65b9\u7a0b\u7ea6\u675f\u6700\u4f18\u63a7\u5236\u95ee\u9898\u7684\u533a\u57df\u5206\u89e3\u65b9\u6cd5","funder_award_id":"11671391","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G26352779","display_name":null,"funder_award_id":"MTM2017-83185-P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G4199071098","display_name":null,"funder_award_id":"91530204","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4348031487","display_name":null,"funder_award_id":"DMS-1217122","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4881361113","display_name":null,"funder_award_id":"MTM2014-57531-P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309482","display_name":"Oklahoma State University","ror":"https://ror.org/045ntgf29"},{"id":"https://openalex.org/F4320309636","display_name":"University of Minnesota","ror":"https://ror.org/03grvy078"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W89839489","https://openalex.org/W1480363740","https://openalex.org/W1968340635","https://openalex.org/W1971610169","https://openalex.org/W1992878096","https://openalex.org/W1998894128","https://openalex.org/W2005268217","https://openalex.org/W2010207646","https://openalex.org/W2012170120","https://openalex.org/W2019529034","https://openalex.org/W2025127681","https://openalex.org/W2030085198","https://openalex.org/W2041304886","https://openalex.org/W2050097488","https://openalex.org/W2053085169","https://openalex.org/W2070586768","https://openalex.org/W2083638730","https://openalex.org/W2092349282","https://openalex.org/W2095060406","https://openalex.org/W2128924369","https://openalex.org/W2132729901","https://openalex.org/W2135572939","https://openalex.org/W2147584861","https://openalex.org/W2220250944","https://openalex.org/W2244594781","https://openalex.org/W2279795488","https://openalex.org/W2285538411","https://openalex.org/W2296275512","https://openalex.org/W2326034009","https://openalex.org/W2460533716","https://openalex.org/W2461866128","https://openalex.org/W2529690472","https://openalex.org/W2607227185","https://openalex.org/W2611709087","https://openalex.org/W2963049391","https://openalex.org/W4239837487","https://openalex.org/W4248903561"],"related_works":[],"abstract_inverted_index":{"In":[0,65],"the":[1,32,35,52,58,62,70,79,100,108],"first":[2],"part":[3],"of":[4,37],"this":[5,66,77],"work,":[6,67],"we":[7,43,68,86],"analyzed":[8],"an":[9,16,46,95],"unconstrained":[10],"Dirichlet":[11],"boundary":[12],"control":[13,53,101],"problem":[14],"for":[15,51,99],"elliptic":[17],"convection":[18],"diffusion":[19],"PDE":[20],"and":[21,60,85,102],"proposed":[22],"a":[23,38,88],"new":[24],"hybridizable":[25],"discontinuous":[26],"Galerkin":[27],"(HDG)":[28],"method":[29],"to":[30,106],"approximate":[31],"solution.":[33],"For":[34],"case":[36],"2D":[39],"convex":[40],"polygonal":[41],"domain,":[42],"also":[44],"proved":[45],"optimal":[47,96],"superlinear":[48],"convergence":[49,71,97,109],"rate":[50,98],"under":[54],"certain":[55],"assumptions":[56],"on":[57,61],"domain":[59],"target":[63],"state.":[64],"revisit":[69],"analysis":[72,90],"without":[73],"these":[74],"assumptions;":[75],"in":[76],"case,":[78],"solution":[80],"can":[81],"have":[82],"low":[83],"regularity,":[84],"use":[87],"different":[89],"approach.":[91],"We":[92],"again":[93],"prove":[94],"present":[103],"numerical":[104],"results":[105],"illustrate":[107],"theory.":[110]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2018-01-12T00:00:00"}
