{"id":"https://openalex.org/W2959359395","doi":"https://doi.org/10.1137/18m1202049","title":"Analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains","display_name":"Analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains","publication_year":2018,"publication_date":"2018-12-01","ids":{"openalex":"https://openalex.org/W2959359395","doi":"https://doi.org/10.1137/18m1202049","mag":"2959359395"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1812.00216","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1812.00216","pdf_url":"https://arxiv.org/pdf/1812.00216","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"},"type":"preprint","indexed_in":["arxiv"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1812.00216","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048905697","display_name":"Keegan L. A. Kirk","orcid":"https://orcid.org/0000-0003-1190-6708"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Kirk, Keegan L. A.","raw_affiliation_strings":["Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046595548","display_name":"Tam\u00e1s Horv\u00e1th","orcid":"https://orcid.org/0000-0001-5294-5362"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Horvath, Tamas L.","raw_affiliation_strings":["Department of Applied Mathematics of the University of Waterloo, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics of the University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036514025","display_name":"Ay\u00e7\u0131l \u00c7e\u015fmeli\u0307o\u011flu","orcid":"https://orcid.org/0000-0001-8057-6349"},"institutions":[{"id":"https://openalex.org/I177721651","display_name":"Oakland University","ror":"https://ror.org/01ythxj32","country_code":"US","type":"education","lineage":["https://openalex.org/I177721651"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cesmelioglu, Aycil","raw_affiliation_strings":["Department of Mathematics and Statistics, Oakland University, Rochester, Michigan 48309, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Oakland University, Rochester, Michigan 48309, USA","institution_ids":["https://openalex.org/I177721651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034917067","display_name":"Sander Rhebergen","orcid":"https://orcid.org/0000-0001-6036-0356"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Rhebergen, Sander","raw_affiliation_strings":["Department of Applied Mathematics of the University of Waterloo, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics of the University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"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":1.0,"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":1.0,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9987999796867371,"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"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9980999827384949,"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":0.7918757200241089},{"id":"https://openalex.org/keywords/space-time","display_name":"Space time","score":0.6086076498031616},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.6062200665473938},{"id":"https://openalex.org/keywords/advection","display_name":"Advection","score":0.5998567342758179},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5797433853149414},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5567467212677002},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5050507187843323},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4952906668186188},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.4659261405467987},{"id":"https://openalex.org/keywords/spacetime","display_name":"Spacetime","score":0.43049031496047974},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.43045711517333984},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42911723256111145},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4290945529937744},{"id":"https://openalex.org/keywords/time-stepping","display_name":"Time stepping","score":0.42432883381843567},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.4111732244491577},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.19330555200576782},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1645096242427826}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7918757200241089},{"id":"https://openalex.org/C96402334","wikidata":"https://www.wikidata.org/wiki/Q3030793","display_name":"Space time","level":2,"score":0.6086076498031616},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.6062200665473938},{"id":"https://openalex.org/C5072599","wikidata":"https://www.wikidata.org/wiki/Q379788","display_name":"Advection","level":2,"score":0.5998567342758179},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5797433853149414},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5567467212677002},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5050507187843323},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4952906668186188},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.4659261405467987},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.43049031496047974},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.43045711517333984},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42911723256111145},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4290945529937744},{"id":"https://openalex.org/C3019693144","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Time stepping","level":3,"score":0.42432883381843567},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.4111732244491577},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.19330555200576782},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1645096242427826},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C42360764","wikidata":"https://www.wikidata.org/wiki/Q83588","display_name":"Chemical engineering","level":1,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:arXiv.org:1812.00216","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1812.00216","pdf_url":"https://arxiv.org/pdf/1812.00216","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1812.00216","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1812.00216","pdf_url":"https://arxiv.org/pdf/1812.00216","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/G287386431","display_name":null,"funder_award_id":"RGPIN\u201005606\u20102015","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G5398251136","display_name":null,"funder_award_id":"RGPAS-478018-2015","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1987196790","https://openalex.org/W1998894128","https://openalex.org/W2003563005","https://openalex.org/W2011538814","https://openalex.org/W2013813162","https://openalex.org/W2041441722","https://openalex.org/W2042418905","https://openalex.org/W2047391773","https://openalex.org/W2052232261","https://openalex.org/W2069058076","https://openalex.org/W2082810159","https://openalex.org/W2130214873","https://openalex.org/W2154720964","https://openalex.org/W2206365535","https://openalex.org/W2493117997","https://openalex.org/W2795471203","https://openalex.org/W2962814658","https://openalex.org/W2963371738","https://openalex.org/W3124380157"],"related_works":["https://openalex.org/W2335200596","https://openalex.org/W1991867815","https://openalex.org/W2133369474","https://openalex.org/W2354715440","https://openalex.org/W2980898237","https://openalex.org/W4299625300","https://openalex.org/W2808682125","https://openalex.org/W1994841366","https://openalex.org/W2524024922","https://openalex.org/W4386556238"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"the":[3,14,35,44,66],"first":[4],"analysis":[5,21],"of":[6,43,75],"a":[7,49,54,62,70],"space--time":[8],"hybridizable":[9],"discontinuous":[10],"Galerkin":[11],"method":[12],"for":[13,73],"advection--diffusion":[15,67],"problem":[16,46,68],"on":[17,24,69],"time-dependent":[18,71],"domains.":[19],"The":[20],"is":[22,59],"based":[23],"non-standard":[25],"local":[26],"trace":[27],"and":[28,37,47],"inverse":[29],"inequalities":[30],"that":[31],"are":[32],"anisotropic":[33],"in":[34,53],"spatial":[36],"time":[38],"steps.":[39],"We":[40],"prove":[41],"well-posedness":[42],"discrete":[45],"provide":[48],"priori":[50],"error":[51],"estimates":[52],"mesh-dependent":[55],"norm.":[56],"Convergence":[57],"theory":[58],"validated":[60],"by":[61],"numerical":[63],"example":[64],"solving":[65],"domain":[72],"approximations":[74],"various":[76],"polynomial":[77],"degree.":[78]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2019-07-23T00:00:00"}