{"id":"https://openalex.org/W2006938047","doi":"https://doi.org/10.1137/s1064827597317636","title":"A Data-Bounded Quadratic Interpolant on Triangles and Tetrahedra","display_name":"A Data-Bounded Quadratic Interpolant on Triangles and Tetrahedra","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2006938047","doi":"https://doi.org/10.1137/s1064827597317636","mag":"2006938047"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827597317636","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827597317636","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5018125253","display_name":"Martin Berzins","orcid":"https://orcid.org/0000-0002-5419-0634"},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Martin Berzins","raw_affiliation_strings":["(University of Leeds"],"affiliations":[{"raw_affiliation_string":"(University of Leeds","institution_ids":["https://openalex.org/I130828816"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5018125253"],"corresponding_institution_ids":["https://openalex.org/I130828816"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.10957533,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"22","issue":"1","first_page":"177","last_page":"197"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9952999949455261,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9952999949455261,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9930999875068665,"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":0.9909999966621399,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6855270862579346},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6852394342422485},{"id":"https://openalex.org/keywords/tetrahedron","display_name":"Tetrahedron","score":0.6818686723709106},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6684018969535828},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6435419321060181},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.566481351852417},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.49578627943992615},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.470342218875885},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.47022318840026855},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.4545140266418457},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.45151638984680176},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4254003167152405},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30058616399765015},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21040990948677063},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1804361641407013}],"concepts":[{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6855270862579346},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6852394342422485},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.6818686723709106},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6684018969535828},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6435419321060181},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.566481351852417},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.49578627943992615},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.470342218875885},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.47022318840026855},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.4545140266418457},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.45151638984680176},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4254003167152405},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30058616399765015},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21040990948677063},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1804361641407013},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s1064827597317636","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827597317636","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1526371444","https://openalex.org/W1548786495","https://openalex.org/W1982820457","https://openalex.org/W2013784064","https://openalex.org/W2032001269","https://openalex.org/W2048956743","https://openalex.org/W2068693617","https://openalex.org/W2109911863","https://openalex.org/W2243974988","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1972096828","https://openalex.org/W2529137940","https://openalex.org/W4302048708","https://openalex.org/W2359913921","https://openalex.org/W3118783749","https://openalex.org/W2002583644","https://openalex.org/W1557607869","https://openalex.org/W4239740410","https://openalex.org/W2366350639","https://openalex.org/W1996195943"],"abstract_inverted_index":{"Many":[0,10],"real-world":[1],"problems":[2,15,27],"are":[3,51],"successfully":[4],"modeled":[5],"by":[6],"partial":[7],"differential":[8],"equations.":[9],"numerical":[11,72],"solvers":[12],"for":[13,53,60],"these":[14],"use":[16],"triangular":[17],"and":[18,31,33,62,84,109],"tetrahedral":[19,116],"meshes":[20],"to":[21,37,63,111],"accurately":[22,43],"model":[23],"complex":[24],"geometries.":[25],"Such":[26],"often":[28],"involve":[29],"shocks":[30],"discontinuities,":[32],"it":[34],"is":[35,82,102],"important":[36],"devise":[38],"interpolation":[39],"methods":[40],"that":[41,81],"can":[42],"approximate":[44],"solutions":[45],"containing":[46],"such":[47],"features.":[48],"These":[49],"interpolants":[50],"required":[52],"the":[54,57,71,93,96,105,112],"postprocessing":[55],"of":[56,92,95,114],"solution,":[58],"e.g.,":[59],"visualization":[61],"recover":[64],"solution":[65],"values":[66,90],"at":[67],"arbitrary":[68],"points":[69],"over":[70],"domain.":[73],"This":[74],"paper":[75],"describes":[76],"a":[77],"triangle-based":[78],"quadratic":[79,107,115],"interpolant":[80,108],"\"data-bounded\"":[83],"so":[85],"will":[86],"not":[87],"create":[88],"any":[89],"outside":[91],"range":[94],"existing":[97],"data":[98],"points.":[99],"The":[100],"method":[101],"compared":[103],"with":[104],"standard":[106],"extended":[110],"case":[113],"elements.":[117]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}