{"id":"https://openalex.org/W7167261336","doi":"https://doi.org/10.48550/arxiv.2607.02362","title":"Sobolev stability of the $L^2$-projection on hybrid meshes","display_name":"Sobolev stability of the $L^2$-projection on hybrid meshes","publication_year":2026,"publication_date":"2026-07-02","ids":{"openalex":"https://openalex.org/W7167261336","doi":"https://doi.org/10.48550/arxiv.2607.02362"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.02362","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.02362","pdf_url":null,"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":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.2607.02362","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010484841","display_name":"Lars Diening","orcid":"https://orcid.org/0000-0002-0523-3079"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Diening, Lars","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139977545","display_name":"Viktoria Lingert","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lingert, Viktoria","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5076638608","display_name":"Tabea Tscherpel","orcid":"https://orcid.org/0000-0002-5899-1279"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tscherpel, Tabea","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":0.4075999855995178,"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":0.4075999855995178,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.11710000038146973,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.08860000222921371,"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":0.753000020980835},{"id":"https://openalex.org/keywords/quadrilateral","display_name":"Quadrilateral","score":0.6916000247001648},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5271999835968018},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5249000191688538},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.45989999175071716},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.40130001306533813},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.3634999990463257},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.33799999952316284}],"concepts":[{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.753000020980835},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7383000254631042},{"id":"https://openalex.org/C151756577","wikidata":"https://www.wikidata.org/wiki/Q36810","display_name":"Quadrilateral","level":3,"score":0.6916000247001648},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5271999835968018},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5249000191688538},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.45989999175071716},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4147999882698059},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.40130001306533813},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.3634999990463257},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34369999170303345},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.33799999952316284},{"id":"https://openalex.org/C170589453","wikidata":"https://www.wikidata.org/wiki/Q7940896","display_name":"Volume mesh","level":4,"score":0.3003999888896942},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.29910001158714294},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.2757999897003174},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.26759999990463257},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.2635999917984009},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2624000012874603},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.260699987411499},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.25949999690055847},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.2558000087738037},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.25369998812675476},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.02362","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.02362","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.02362","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.02362","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"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":{"We":[0],"establish":[1],"$L^p$-":[2],"and":[3,19,52,61,92],"$W^{1,p}$-stability":[4],"of":[5,17,34,36,78,86],"the":[6,30,37,50,67,87],"$L^2$-projection":[7],"onto":[8],"mapped":[9],"Lagrange":[10],"finite":[11],"elements":[12],"on":[13,83],"hybrid":[14],"meshes":[15,76],"consisting":[16,77],"triangles":[18],"convex":[20,97],"quadrilaterals":[21],"arising":[22],"from":[23],"adaptive":[24],"mesh":[25],"refinement.":[26],"If":[27],"$K$":[28],"is":[29],"(tensor":[31],"product)":[32],"degree":[33],"polynomials":[35],"discretisation,":[38],"then":[39],"we":[40],"show,":[41],"in":[42],"particular,":[43],"$W^{1,2}$-stability":[44],"for":[45,49,66,74],"all":[46],"$K\\geq":[47],"2$":[48],"Q-RG":[51],"Q-RB":[53],"refinements.":[54],"This":[55],"extends":[56],"results":[57],"by":[58,89],"Ali,":[59],"Funken,":[60],"Schmidt":[62],"(2022)":[63],"which":[64],"hold":[65],"range":[68],"$2":[69],"\\leq":[70,72],"K":[71],"9$":[73],"initial":[75],"parallelograms.":[79],"Our":[80],"proof":[81],"relies":[82],"an":[84],"extension":[85],"technique":[88],"Diening,":[90],"Storn":[91],"Tscherpel":[93],"(2021)":[94],"to":[95],"general":[96],"quadrilaterals.":[98]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-04T00:00:00"}
