{"id":"https://openalex.org/W7135016328","doi":"https://doi.org/10.48550/arxiv.2603.10754","title":"On the consistency of the Domain of Dependence cut cell stabilization","display_name":"On the consistency of the Domain of Dependence cut cell stabilization","publication_year":2026,"publication_date":"2026-03-11","ids":{"openalex":"https://openalex.org/W7135016328","doi":"https://doi.org/10.48550/arxiv.2603.10754"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.10754","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.10754","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.10754","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128806119","display_name":"Gunnar Birke","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Birke, Gunnar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083989030","display_name":"Christian Engwer","orcid":"https://orcid.org/0000-0002-6041-8228"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Engwer, Christian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026383841","display_name":"Jan Giesselmann","orcid":"https://orcid.org/0009-0008-0217-7244"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Giesselmann, Jan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5071317182","display_name":"Sandra May","orcid":"https://orcid.org/0000-0001-9178-6595"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"May, Sandra","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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":0.7218000292778015,"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":0.7218000292778015,"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":0.10639999806880951,"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":0.035100001841783524,"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/polygon-mesh","display_name":"Polygon mesh","score":0.6888999938964844},{"id":"https://openalex.org/keywords/cartesian-coordinate-system","display_name":"Cartesian coordinate system","score":0.6571000218391418},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.5604000091552734},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5536999702453613},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5404999852180481},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5203999876976013},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.41920000314712524},{"id":"https://openalex.org/keywords/hinge","display_name":"Hinge","score":0.4117000102996826},{"id":"https://openalex.org/keywords/degree-of-a-polynomial","display_name":"Degree of a polynomial","score":0.37630000710487366}],"concepts":[{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.6888999938964844},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.6571000218391418},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.603600025177002},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5604000091552734},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5536999702453613},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5404999852180481},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5325999855995178},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5203999876976013},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.41920000314712524},{"id":"https://openalex.org/C44000306","wikidata":"https://www.wikidata.org/wiki/Q244330","display_name":"Hinge","level":2,"score":0.4117000102996826},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.37630000710487366},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3747999966144562},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3732999861240387},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.35659998655319214},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.34130001068115234},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3294999897480011},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.32420000433921814},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.30489999055862427},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29760000109672546},{"id":"https://openalex.org/C31388003","wikidata":"https://www.wikidata.org/wiki/Q7624548","display_name":"Strong consistency","level":3,"score":0.2867000102996826},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.2856999933719635},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28290000557899475},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.2791999876499176},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C103824480","wikidata":"https://www.wikidata.org/wiki/Q185889","display_name":"Time domain","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C137105694","wikidata":"https://www.wikidata.org/wiki/Q3407510","display_name":"Local consistency","level":4,"score":0.2522999942302704}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.10754","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.10754","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.10754","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.10754","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"So":[0],"called":[1],"cartesian":[2],"cut":[3,47],"cell":[4],"meshes":[5,11],"provide":[6],"efficient":[7],"ways":[8],"to":[9,18,43],"generate":[10],"but":[12],"do":[13,101],"require":[14],"tailored":[15],"numerical":[16,99],"methods":[17],"not":[19],"suffer":[20],"from":[21],"stabilization":[22,64,136],"issues,":[23],"especially":[24],"in":[25,93,150,165],"the":[26,30,55,73,94,106,134,154,162,166],"hyperbolic":[27],"regime":[28],"where":[29],"application":[31],"of":[32,61,80,146,161],"explicit":[33],"time":[34,56,68],"stepping":[35],"schemes":[36],"is":[37,52],"common.":[38],"In":[39,125],"this":[40,103,109,126],"scenario,":[41],"due":[42],"potentially":[44],"arbitrarily":[45],"small":[46],"cells,":[48],"an":[49,78,138,143],"infeasible":[50],"restriction":[51],"imposed":[53],"on":[54,72,105,121],"step":[57,69],"size.":[58],"The":[59],"Domain":[60],"Dependence":[62],"(DoD)":[63],"allows":[65],"for":[66,115,133],"a":[67,81,122,131,157],"size":[70],"based":[71],"underlying":[74],"Cartesian":[75],"mesh.":[76],"Being":[77],"extension":[79],"discontinuous":[82],"Galerkin":[83],"(DG)":[84],"method,":[85],"one":[86],"would":[87],"expect":[88],"similar":[89],"accuracy":[90],"properties":[91],"as":[92],"pure":[95],"DG":[96],"case.":[97,168],"While":[98],"results":[100],"support":[102],"expectation,":[104],"analytical":[107],"level":[108],"has":[110],"only":[111],"been":[112],"investigated":[113],"thoroughly":[114],"$k=0$.":[116],"Error":[117],"analysis":[118,160],"typically":[119],"hinges":[120],"consistency":[123],"result.":[124],"contribution":[127],"we":[128],"prove":[129],"such":[130],"result":[132],"DoD":[135],"given":[137],"arbitrary":[139],"polynomial":[140],"degree":[141],"and":[142],"exact":[144],"solution":[145],"sufficient":[147],"regularity.":[148],"This":[149],"turn":[151],"could":[152],"open":[153],"way":[155],"towards":[156],"more":[158],"refined":[159],"method":[163],"even":[164],"high-order":[167]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-13T00:00:00"}
