{"id":"https://openalex.org/W4317384287","doi":"https://doi.org/10.1090/mcom/3824","title":"Interpolation operator on negative Sobolev spaces","display_name":"Interpolation operator on negative Sobolev spaces","publication_year":2023,"publication_date":"2023-01-18","ids":{"openalex":"https://openalex.org/W4317384287","doi":"https://doi.org/10.1090/mcom/3824"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3824","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3824","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010484841","display_name":"Lars Diening","orcid":"https://orcid.org/0000-0002-0523-3079"},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Lars Diening","raw_affiliation_strings":["Department of Mathematics, Bielefeld University, Postfach 10 01 31, 33501 Bielefeld, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bielefeld University, Postfach 10 01 31, 33501 Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089019825","display_name":"Johannes Storn","orcid":"https://orcid.org/0000-0003-1520-6557"},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Johannes Storn","raw_affiliation_strings":["Department of Mathematics, Bielefeld University, Postfach 10 01 31, 33501 Bielefeld, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bielefeld University, Postfach 10 01 31, 33501 Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076638608","display_name":"Tabea Tscherpel","orcid":"https://orcid.org/0000-0002-5899-1279"},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technical University of Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tabea Tscherpel","raw_affiliation_strings":["Department of Mathematics, Technische Universit\u00c3\u00a4t Darmstadt, Dolivostra\u00c3\u009fe 15, 64293 Darmstadt, Germany","Department of Mathematics, Technische Universit\u00e4t Darmstadt, Dolivostra\u00dfe 15, 64293 Darmstadt, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technische Universit\u00c3\u00a4t Darmstadt, Dolivostra\u00c3\u009fe 15, 64293 Darmstadt, Germany","institution_ids":["https://openalex.org/I31512782"]},{"raw_affiliation_string":"Department of Mathematics, Technische Universit\u00e4t Darmstadt, Dolivostra\u00dfe 15, 64293 Darmstadt, Germany","institution_ids":["https://openalex.org/I31512782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5010484841"],"corresponding_institution_ids":["https://openalex.org/I20121455"],"apc_list":null,"apc_paid":null,"fwci":1.73,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.80511247,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"92","issue":"342","first_page":"1511","last_page":"1541"},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9993000030517578,"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":0.9993000030517578,"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/mathematics","display_name":"Mathematics","score":0.9203424453735352},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.7215936183929443},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6171107292175293},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6074303388595581},{"id":"https://openalex.org/keywords/lagrange-polynomial","display_name":"Lagrange polynomial","score":0.4810076653957367},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4404264986515045},{"id":"https://openalex.org/keywords/polynomial-interpolation","display_name":"Polynomial interpolation","score":0.423404723405838},{"id":"https://openalex.org/keywords/dual-polyhedron","display_name":"Dual polyhedron","score":0.41807544231414795},{"id":"https://openalex.org/keywords/operator-norm","display_name":"Operator norm","score":0.41775017976760864},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3957536518573761},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38924065232276917},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3764473795890808},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.3425835371017456},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.33567339181900024},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.29044580459594727},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1414109468460083},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.11120489239692688}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9203424453735352},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.7215936183929443},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6171107292175293},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6074303388595581},{"id":"https://openalex.org/C64208722","wikidata":"https://www.wikidata.org/wiki/Q861606","display_name":"Lagrange polynomial","level":3,"score":0.4810076653957367},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4404264986515045},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.423404723405838},{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.41807544231414795},{"id":"https://openalex.org/C68386474","wikidata":"https://www.wikidata.org/wiki/Q980557","display_name":"Operator norm","level":3,"score":0.41775017976760864},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3957536518573761},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38924065232276917},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3764473795890808},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.3425835371017456},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.33567339181900024},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.29044580459594727},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1414109468460083},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.11120489239692688},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/3824","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3824","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1521959696","display_name":null,"funder_award_id":"SFB 1283/2 2021\u00e2??317210226","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W1555557982","https://openalex.org/W1815636265","https://openalex.org/W1967364504","https://openalex.org/W1980404981","https://openalex.org/W1986054947","https://openalex.org/W1993077381","https://openalex.org/W2009985306","https://openalex.org/W2030028670","https://openalex.org/W2051043245","https://openalex.org/W2055962135","https://openalex.org/W2061988259","https://openalex.org/W2072811159","https://openalex.org/W2076074132","https://openalex.org/W2084672174","https://openalex.org/W2092037996","https://openalex.org/W2107813568","https://openalex.org/W2114612290","https://openalex.org/W2199169705","https://openalex.org/W2227629823","https://openalex.org/W2300734653","https://openalex.org/W2322620490","https://openalex.org/W2402468387","https://openalex.org/W2463821656","https://openalex.org/W2555522850","https://openalex.org/W2577131966","https://openalex.org/W2761307852","https://openalex.org/W2764183206","https://openalex.org/W2765080741","https://openalex.org/W2811411416","https://openalex.org/W2893822386","https://openalex.org/W2907152173","https://openalex.org/W2913877309","https://openalex.org/W2962763863","https://openalex.org/W2963017886","https://openalex.org/W2963817075","https://openalex.org/W3014945572","https://openalex.org/W3016323595","https://openalex.org/W3112398217","https://openalex.org/W3118722523","https://openalex.org/W3135337288","https://openalex.org/W3153057007","https://openalex.org/W3156968244","https://openalex.org/W3168713754","https://openalex.org/W3202771958","https://openalex.org/W3204708751","https://openalex.org/W3209915062","https://openalex.org/W3215334222","https://openalex.org/W4205815276","https://openalex.org/W4242775668","https://openalex.org/W4245007249","https://openalex.org/W4250831033"],"related_works":["https://openalex.org/W1179085681","https://openalex.org/W2374545223","https://openalex.org/W2095809698","https://openalex.org/W2371738094","https://openalex.org/W2354378723","https://openalex.org/W4200281652","https://openalex.org/W2387259408","https://openalex.org/W4367556995","https://openalex.org/W2488705107","https://openalex.org/W2349741627"],"abstract_inverted_index":{"We":[0,49],"introduce":[1],"a":[2,75],"Scott\u2013Zhang":[3],"type":[4],"projection":[5],"operator":[6,22,60],"mapping":[7],"to":[8,17],"Lagrange":[9],"elements":[10],"for":[11,44,66],"arbitrary":[12],"polynomial":[13],"order.":[14],"In":[15],"addition":[16],"the":[18,38,59],"usual":[19],"properties,":[20],"this":[21],"is":[23,35],"compatible":[24],"with":[25,53],"duals":[26],"of":[27,47,58],"first":[28],"order":[29],"Sobolev":[30],"spaces.":[31],"More":[32],"specifically,":[33],"it":[34],"stable":[36],"in":[37,74],"corresponding":[39],"negative":[40],"norms":[41],"and":[42,69],"allows":[43],"optimal":[45],"rates":[46],"convergence.":[48],"discuss":[50],"alternative":[51],"operators":[52],"similar":[54],"properties.":[55],"As":[56],"applications":[57],"we":[61],"prove":[62],"interpolation":[63],"error":[64],"estimates":[65],"parabolic":[67],"problems":[68],"smoothen":[70],"rough":[71],"right-hand":[72],"sides":[73],"least":[76],"squares":[77],"finite":[78],"element":[79],"method.":[80]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}