{"id":"https://openalex.org/W7156300473","doi":"https://doi.org/10.48550/arxiv.2604.22543","title":"On a Hybrid Mixed Domain Decomposition Method","display_name":"On a Hybrid Mixed Domain Decomposition Method","publication_year":2026,"publication_date":"2026-04-24","ids":{"openalex":"https://openalex.org/W7156300473","doi":"https://doi.org/10.48550/arxiv.2604.22543"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.22543","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.22543","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.22543","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134664012","display_name":"Kersten Schmidt","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schmidt, Kersten","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134721033","display_name":"Timon Seibel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Seibel, Timon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5054323051","display_name":"Sebastian Sch\u00f6ps","orcid":"https://orcid.org/0000-0001-9150-0219"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sch\u00f6ps, Sebastian","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":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":0.9581999778747559,"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":0.9581999778747559,"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/T10514","display_name":"Numerical methods in engineering","score":0.012900000438094139,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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":0.01209999993443489,"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/finite-element-method","display_name":"Finite element method","score":0.6953999996185303},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6876999735832214},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6700000166893005},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6226999759674072},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5698000192642212},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.5242999792098999},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.5228000283241272},{"id":"https://openalex.org/keywords/quadrilateral","display_name":"Quadrilateral","score":0.4747999906539917},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.45660001039505005}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8068000078201294},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6953999996185303},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6876999735832214},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6700000166893005},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6226999759674072},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5698000192642212},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.5242999792098999},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5228000283241272},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5080999732017517},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5002999901771545},{"id":"https://openalex.org/C151756577","wikidata":"https://www.wikidata.org/wiki/Q36810","display_name":"Quadrilateral","level":3,"score":0.4747999906539917},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.45660001039505005},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.4058000147342682},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.39430001378059387},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.37380000948905945},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.35530000925064087},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.3472000062465668},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.34060001373291016},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.3303000032901764},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.3285999894142151},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.3043000102043152},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.2858000099658966},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.2840999960899353},{"id":"https://openalex.org/C38961997","wikidata":"https://www.wikidata.org/wiki/Q7575186","display_name":"Spectral element method","level":4,"score":0.27379998564720154},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.27320000529289246},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.26969999074935913}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.22543","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.22543","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.22543","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.22543","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,136],"present":[1],"a":[2,43,49,104],"domain":[3,21],"decomposition":[4,22],"formulation":[5,47,56],"based":[6,41],"on":[7,42,70,81,164,222],"hybridization":[8],"which":[9,144],"is":[10,40,95,145],"inspired":[11],"by":[12,24,86],"hybridized":[13],"discontinuous":[14,29],"Galerkin":[15,30,51,93],"(HDG)":[16],"methods,":[17,31],"that":[18,108],"enhance":[19],"mixed":[20],"methods":[23],"incorporating":[25],"stabilization":[26,149,224],"terms.":[27],"Unlike":[28],"our":[32],"analysis":[33,139,183],"of":[34,76,90,101,109,140,162,173,178,233],"the":[35,54,57,71,74,77,82,91,110,114,123,130,141,148,169,181,186,200,205,209,215,218,223,227],"proposed":[36],"finite":[37,78,115,159],"element":[38,79,116,160],"method":[39,94,117],"corresponding":[44],"consistent":[45],"variational":[46,55,111],"and":[48,126,132,207,226],"perturbed":[50,92],"method.":[52],"In":[53,180],"divergence":[58],"appears":[59],"not":[60],"only":[61],"within":[62],"subdomains,":[63],"but":[64],"also":[65],"as":[66],"an":[67,98,138,230],"$L^2$-surface":[68],"quantity":[69],"interfaces.":[72],"Furthermore,":[73],"traces":[75],"functions":[80],"interfaces":[83],"are":[84,212],"replaced":[85],"$L^2$-distributions.":[87],"The":[88],"well-posedness":[89],"shown":[96],"for":[97,122,129,154,175,196,204,208],"appropriate":[99],"choice":[100],"subspaces,":[102],"in":[103,147,193],"manner":[105],"similar":[106],"to":[107,189],"formulation.":[112],"For":[113,214],"we":[118,184],"use":[119],"Raviart-Thomas":[120],"elements":[121],"dual":[124,216],"variable":[125,217],"piecewise":[127,155],"polynomials":[128],"primal":[131,206],"hybrid":[133,210],"variables,":[134],"respectively.":[135],"perform":[137],"discretization":[142,187],"error":[143,182,188],"explicit":[146],"parameter":[150,225],"$\u03c4$.":[151,179,194],"Numerical":[152],"experiments":[153],"smooth":[156],"solutions":[157],"using":[158],"spaces":[161],"order~$q$":[163],"curved":[165],"quadrilateral":[166],"meshes":[167],"confirm":[168],"predicted":[170],"convergence":[171,202,219],"rate":[172,220,232],"$q+1$":[174],"small":[176],"values":[177,199],"observe":[185],"be":[190],"uniformly":[191],"bounded":[192],"Even":[195],"large":[197],"$\u03c4$":[198],"observed":[201],"rates":[203],"variables":[211],"$q+1$.":[213],"depends":[221],"mesh-width,":[228],"with":[229],"asymptotic":[231],"$q+\\tfrac12$.":[234]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-28T00:00:00"}