{"id":"https://openalex.org/W4387874098","doi":"https://doi.org/10.3390/axioms12101002","title":"Nonlinear 2D C1 Quadratic Spline Quasi-Interpolants on Triangulations for the Approximation of Piecewise Smooth Functions","display_name":"Nonlinear 2D C1 Quadratic Spline Quasi-Interpolants on Triangulations for the Approximation of Piecewise Smooth Functions","publication_year":2023,"publication_date":"2023-10-23","ids":{"openalex":"https://openalex.org/W4387874098","doi":"https://doi.org/10.3390/axioms12101002"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12101002","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12101002","pdf_url":"https://www.mdpi.com/2075-1680/12/10/1002/pdf?version=1698068960","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/10/1002/pdf?version=1698068960","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076094492","display_name":"Francesc Ar\u00e0ndiga","orcid":"https://orcid.org/0000-0001-9228-4159"},"institutions":[{"id":"https://openalex.org/I16097986","display_name":"Universitat de Val\u00e8ncia","ror":"https://ror.org/043nxc105","country_code":"ES","type":"education","lineage":["https://openalex.org/I16097986"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Francesc Ar\u00e0ndiga","raw_affiliation_strings":["Departament of Mathematics, Universitat de Val\u00e8ncia, Av. Vicent Andr\u00e9s Estell\u00e9s, E-46100 Burjassot, Spain"],"raw_orcid":"https://orcid.org/0000-0001-9228-4159","affiliations":[{"raw_affiliation_string":"Departament of Mathematics, Universitat de Val\u00e8ncia, Av. Vicent Andr\u00e9s Estell\u00e9s, E-46100 Burjassot, Spain","institution_ids":["https://openalex.org/I16097986"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039926993","display_name":"Sara Remogna","orcid":"https://orcid.org/0000-0003-4259-1657"},"institutions":[{"id":"https://openalex.org/I1330701686","display_name":"Collegio Carlo Alberto","ror":"https://ror.org/0397knh37","country_code":"IT","type":"education","lineage":["https://openalex.org/I1330701686"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Sara Remogna","raw_affiliation_strings":["Department of Mathematics, University of Torino, Via Carlo Alberto 10, 10123 Torino, Italy","Department of Mathematics \"G. Peano\", University of Torino, Via Carlo Alberto 10, 10123 Torino, Italy"],"raw_orcid":"https://orcid.org/0000-0003-4259-1657","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Torino, Via Carlo Alberto 10, 10123 Torino, Italy","institution_ids":["https://openalex.org/I1330701686"]},{"raw_affiliation_string":"Department of Mathematics \"G. Peano\", University of Torino, Via Carlo Alberto 10, 10123 Torino, Italy","institution_ids":["https://openalex.org/I1330701686"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039926993"],"corresponding_institution_ids":["https://openalex.org/I1330701686"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.0065,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.71764739,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"12","issue":"10","first_page":"1002","last_page":"1002"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9995999932289124,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9995999932289124,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9925000071525574,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9685999751091003,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.7767730951309204},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.7712432146072388},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7541285753250122},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.7036041021347046},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6775035858154297},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6104078888893127},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.5305269956588745},{"id":"https://openalex.org/keywords/gibbs-phenomenon","display_name":"Gibbs phenomenon","score":0.49843716621398926},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48119503259658813},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44848641753196716},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42681172490119934},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2441195547580719},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09116408228874207}],"concepts":[{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.7767730951309204},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.7712432146072388},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7541285753250122},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.7036041021347046},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6775035858154297},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6104078888893127},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.5305269956588745},{"id":"https://openalex.org/C149568634","wikidata":"https://www.wikidata.org/wiki/Q5374","display_name":"Gibbs phenomenon","level":3,"score":0.49843716621398926},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48119503259658813},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44848641753196716},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42681172490119934},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2441195547580719},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09116408228874207},{"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/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms12101002","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12101002","pdf_url":"https://www.mdpi.com/2075-1680/12/10/1002/pdf?version=1698068960","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:561769051a9842d5b945ff0af7a83f43","is_oa":true,"landing_page_url":"https://doaj.org/article/561769051a9842d5b945ff0af7a83f43","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 10, p 1002 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms12101002","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12101002","pdf_url":"https://www.mdpi.com/2075-1680/12/10/1002/pdf?version=1698068960","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4514638491","display_name":null,"funder_award_id":"CIAICO/2021/227","funder_id":"https://openalex.org/F4320321864","funder_display_name":"Generalitat Valenciana"},{"id":"https://openalex.org/G8139860","display_name":null,"funder_award_id":"PID2020-117211GB-I00","funder_id":"https://openalex.org/F4320321864","funder_display_name":"Generalitat Valenciana"}],"funders":[{"id":"https://openalex.org/F4320321864","display_name":"Generalitat Valenciana","ror":"https://ror.org/0097mvx21"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4387874098.pdf"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W287434204","https://openalex.org/W1608707775","https://openalex.org/W1998706659","https://openalex.org/W2039150507","https://openalex.org/W2041195280","https://openalex.org/W2069100091","https://openalex.org/W2072568837","https://openalex.org/W2075868810","https://openalex.org/W2076775844","https://openalex.org/W2084413738","https://openalex.org/W2155674512","https://openalex.org/W2162499410","https://openalex.org/W2566785243","https://openalex.org/W2567032824","https://openalex.org/W3002902953","https://openalex.org/W4200144631","https://openalex.org/W4205493247","https://openalex.org/W4213444854","https://openalex.org/W4214771884","https://openalex.org/W4220842341","https://openalex.org/W4233782503","https://openalex.org/W4252664964","https://openalex.org/W4285498562","https://openalex.org/W4289133682","https://openalex.org/W4295996101","https://openalex.org/W4323111927"],"related_works":["https://openalex.org/W2086188421","https://openalex.org/W591014930","https://openalex.org/W1972096828","https://openalex.org/W2953303953","https://openalex.org/W2380529683","https://openalex.org/W2069818228","https://openalex.org/W2130355919","https://openalex.org/W1029391197","https://openalex.org/W3200580474","https://openalex.org/W4387874098"],"abstract_inverted_index":{"The":[0],"aim":[1],"of":[2,23,71],"this":[3],"paper":[4],"is":[5],"to":[6,48,54],"present":[7],"and":[8,59,75,80],"study":[9,67],"nonlinear":[10],"bivariate":[11],"C1":[12],"quadratic":[13],"spline":[14,31],"quasi-interpolants":[15,51,74],"on":[16],"uniform":[17],"criss-cross":[18],"triangulations":[19],"for":[20],"the":[21,33,68,72,84],"approximation":[22],"piecewise":[24],"smooth":[25,64],"functions.":[26],"Indeed,":[27],"by":[28],"using":[29],"classical":[30,50],"quasi-interpolants,":[32],"Gibbs":[34],"phenomenon":[35],"appears":[36],"when":[37],"approximating":[38],"near":[39,57],"discontinuities.":[40],"Here,":[41],"we":[42,76],"use":[43],"weighted":[44],"essentially":[45],"non-oscillatory":[46],"techniques":[47],"modify":[49],"in":[52,63],"order":[53],"avoid":[55],"oscillations":[56],"discontinuities":[58],"maintain":[60],"high-order":[61],"accuracy":[62],"regions.":[65],"We":[66],"convergence":[69],"properties":[70],"proposed":[73],"provide":[77],"some":[78],"numerical":[79],"graphical":[81],"tests":[82],"confirming":[83],"theoretical":[85],"results.":[86]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2023-10-24T00:00:00"}