{"id":"https://openalex.org/W2793775085","doi":"https://doi.org/10.1137/18m1176798","title":"Projection-Based Finite Elements for Nonlinear Function Spaces","display_name":"Projection-Based Finite Elements for Nonlinear Function Spaces","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2793775085","doi":"https://doi.org/10.1137/18m1176798","mag":"2793775085"},"language":"en","primary_location":{"id":"doi:10.1137/18m1176798","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1176798","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1803.06576","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023888160","display_name":"Philipp Grohs","orcid":"https://orcid.org/0000-0001-9205-0969"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Philipp Grohs","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042691754","display_name":"Hanne Hardering","orcid":"https://orcid.org/0009-0002-8173-7807"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hanne Hardering","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082524584","display_name":"Oliver Sander","orcid":"https://orcid.org/0000-0003-1093-6374"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Oliver Sander","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-1093-6374","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5036837080","display_name":"Markus Sprecher","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Markus Sprecher","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":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00488291,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"57","issue":"1","first_page":"404","last_page":"428"},"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":0.9991000294685364,"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":0.9991000294685364,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9979000091552734,"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":0.9977999925613403,"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":0.8179066181182861},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.6081894040107727},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.598577082157135},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5743029117584229},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5026628971099854},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.4863872826099396},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.48554369807243347},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.4750918447971344},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.45747730135917664},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4521888792514801},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.44913309812545776},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4172408878803253},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4148891270160675},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3993348479270935},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11545699834823608},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07320201396942139},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.06878131628036499}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8179066181182861},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.6081894040107727},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.598577082157135},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5743029117584229},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5026628971099854},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4863872826099396},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.48554369807243347},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4750918447971344},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.45747730135917664},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4521888792514801},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.44913309812545776},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4172408878803253},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4148891270160675},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3993348479270935},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11545699834823608},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07320201396942139},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.06878131628036499},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/18m1176798","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1176798","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1803.06576","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1803.06576","pdf_url":"https://arxiv.org/pdf/1803.06576","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":"","raw_type":"text"},{"id":"pmh:oai:arXiv.org:1803.06576","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1803.06576","pdf_url":"https://arxiv.org/pdf/1803.06576","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"},{"id":"mag:2793775085","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1803.06576","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1803.06576","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1803.06576","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":"pmh:oai:arXiv.org:1803.06576","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1803.06576","pdf_url":"https://arxiv.org/pdf/1803.06576","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2793775085.pdf","grobid_xml":"https://content.openalex.org/works/W2793775085.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W1448623749","https://openalex.org/W1487446337","https://openalex.org/W1488292173","https://openalex.org/W1490315654","https://openalex.org/W1557324374","https://openalex.org/W1635574198","https://openalex.org/W1755177043","https://openalex.org/W1804110266","https://openalex.org/W1978913015","https://openalex.org/W1979710921","https://openalex.org/W1982223847","https://openalex.org/W1982954645","https://openalex.org/W1983496390","https://openalex.org/W1985698122","https://openalex.org/W1986120564","https://openalex.org/W1991670087","https://openalex.org/W1995506626","https://openalex.org/W1999212791","https://openalex.org/W2001133651","https://openalex.org/W2001669569","https://openalex.org/W2010769900","https://openalex.org/W2015660465","https://openalex.org/W2019798593","https://openalex.org/W2084966478","https://openalex.org/W2088307891","https://openalex.org/W2096610373","https://openalex.org/W2102635728","https://openalex.org/W2124673822","https://openalex.org/W2125883408","https://openalex.org/W2129261057","https://openalex.org/W2152394501","https://openalex.org/W2231872218","https://openalex.org/W2289110059","https://openalex.org/W2510235145","https://openalex.org/W2550189521","https://openalex.org/W2577603277","https://openalex.org/W2770190057","https://openalex.org/W2963207505","https://openalex.org/W2964029910"],"related_works":["https://openalex.org/W2021969763","https://openalex.org/W2161897368","https://openalex.org/W3125331871","https://openalex.org/W77166905","https://openalex.org/W2051618593","https://openalex.org/W902619230","https://openalex.org/W2539058769","https://openalex.org/W2054624753","https://openalex.org/W2963017886","https://openalex.org/W2907152173","https://openalex.org/W3103056772","https://openalex.org/W2094648722","https://openalex.org/W2066686684","https://openalex.org/W2163652238","https://openalex.org/W1483658743","https://openalex.org/W3095371466","https://openalex.org/W1968480758","https://openalex.org/W3153006547","https://openalex.org/W1989401107","https://openalex.org/W2963879089"],"abstract_inverted_index":{"We":[0,37],"introduce":[1],"a":[2,13,26,68,85,89],"novel":[3],"type":[4],"of":[5,61],"approximation":[6],"spaces":[7],"for":[8,55,81],"functions":[9,18],"with":[10,43,67],"values":[11],"in":[12,25],"nonlinear":[14,69],"manifold.":[15,36,91],"The":[16],"discrete":[17,62],"are":[19,96],"constructed":[20],"by":[21],"piecewise":[22],"polynomial":[23],"interpolation":[24,40],"Euclidean":[27],"embedding":[28],"space,":[29],"and":[30,47,76],"then":[31],"projected":[32],"pointwise":[33],"onto":[34],"the":[35,56],"show":[38,52],"optimal":[39,74],"error":[41,79,94],"bounds":[42,54,80,95],"respect":[44],"to":[45],"Lebesgue":[46],"Sobolev":[48],"norms.":[49],"Additionally,":[50],"we":[51,72],"similar":[53],"test":[57],"functions,":[58],"i.e.,":[59],"variations":[60],"functions.":[63],"Combining":[64],"these":[65,93],"results":[66],"C\u00e9a":[70],"lemma,":[71],"prove":[73],"$L^2$":[75],"$H^1$":[77],"discretization":[78],"harmonic":[82],"maps":[83],"from":[84],"planar":[86],"domain":[87],"into":[88],"smooth":[90],"All":[92],"also":[97],"verified":[98],"numerically.":[99]},"counts_by_year":[],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}