{"id":"https://openalex.org/W1971340088","doi":"https://doi.org/10.1137/060667992","title":"An Interpolation Error Estimate on Anisotropic Meshes in ${\\mathcalR}^{n}$ and Optimal Metrics for Mesh Refinement","display_name":"An Interpolation Error Estimate on Anisotropic Meshes in ${\\mathcalR}^{n}$ and Optimal Metrics for Mesh Refinement","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1971340088","doi":"https://doi.org/10.1137/060667992","mag":"1971340088"},"language":"en","primary_location":{"id":"doi:10.1137/060667992","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060667992","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":["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/A5112064417","display_name":"Weiming Cao","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Weiming Cao","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5112064417"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5641,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.87703815,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"45","issue":"6","first_page":"2368","last_page":"2391"},"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":0.9993000030517578,"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":0.9993000030517578,"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":0.9925000071525574,"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/T11366","display_name":"Elasticity and Material Modeling","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/mathematics","display_name":"Mathematics","score":0.8037785291671753},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.6136483550071716},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5530494451522827},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5460621118545532},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5375473499298096},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.5107927322387695},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4698580503463745},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4316127300262451},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.41953301429748535},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38368797302246094},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2582956552505493},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10481739044189453}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8037785291671753},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.6136483550071716},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5530494451522827},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5460621118545532},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5375473499298096},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.5107927322387695},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4698580503463745},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4316127300262451},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.41953301429748535},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38368797302246094},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2582956552505493},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10481739044189453},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/060667992","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060667992","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1566833591","https://openalex.org/W1973071447","https://openalex.org/W1975932797","https://openalex.org/W1979518155","https://openalex.org/W1992595544","https://openalex.org/W1995404822","https://openalex.org/W2003049157","https://openalex.org/W2030982479","https://openalex.org/W2032350951","https://openalex.org/W2042199582","https://openalex.org/W2044892973","https://openalex.org/W2064364918","https://openalex.org/W2071415238","https://openalex.org/W2072559684","https://openalex.org/W2081179467","https://openalex.org/W2085045785","https://openalex.org/W2091354775","https://openalex.org/W2106828713","https://openalex.org/W2112311198","https://openalex.org/W2136969662","https://openalex.org/W2142693250","https://openalex.org/W2324833387","https://openalex.org/W2328632875","https://openalex.org/W2505585705","https://openalex.org/W3144493338","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2611031068","https://openalex.org/W1704347466","https://openalex.org/W1996936972","https://openalex.org/W4283017538","https://openalex.org/W1545275724","https://openalex.org/W2802707792","https://openalex.org/W2569979269","https://openalex.org/W2075777916","https://openalex.org/W3021699548","https://openalex.org/W4291718021"],"abstract_inverted_index":{"In":[0],"this":[1,145],"paper,":[2],"we":[3,54,94,111],"extend":[4],"the":[5,21,29,37,41,47,51,74,97,103,119,139,151,162],"work":[6],"in":[7,36,107,144],"[W.":[8],"Cao,":[9],"Math.":[10,84],"Comp.,":[11],"to":[12,14,102,117],"appear]":[13],"functions":[15],"of":[16,24,40],"n":[17],"dimensions.":[18],"We":[19,123],"measure":[20,49,121],"anisotropic":[22,48,120,135],"behavior":[23],"higher-order":[25],"derivative":[26],"tensors":[27],"by":[28],"\u201clargest\u201d":[30],"(in":[31],"certain":[32],"sense)":[33],"ellipse/ellipsoid":[34],"contained":[35],"level":[38],"curve/surface":[39],"polynomial":[42,61],"for":[43,50,59,77,128,161],"directional":[44],"derivatives.":[45],"Given":[46],"interpolated":[52],"functions,":[53],"derive":[55],"an":[56],"error":[57,105,154,164],"estimate":[58],"piecewise":[60],"interpolations":[62],"on":[63,133,158],"meshes":[64,136,159],"that":[65,150],"are":[66],"quasi-uniform":[67],"under":[68],"a":[69,113],"given":[70],"metric.":[71],"By":[72],"using":[73],"inertia":[75],"properties":[76],"matrix":[78],"eigenvalues":[79],"[R.":[80],"C.":[81],"Thompson,":[82],"J.":[83],"Anal.":[85],"Appl.,":[86],"58":[87],"(1977),":[88],"pp.":[89],"572\u2013577]":[90],"and":[91,130],"H\u00f6lder's":[92],"inequality,":[93],"can":[95],"identify":[96],"optimal":[98,140,160],"mesh":[99,141],"metrics":[100,142],"leading":[101],"smallest":[104,152],"bound":[106],"various":[108,134],"norms.":[109],"Furthermore,":[110],"develop":[112],"dimensional":[114],"reduction":[115],"method":[116],"find":[118],"approximately.":[122],"present":[124],"two":[125],"numerical":[126],"examples":[127],"linear":[129],"quadratic":[131],"interpolation":[132,153],"generated":[137],"with":[138],"developed":[143],"paper.":[146],"Numerical":[147],"results":[148],"show":[149],"is":[155],"attained":[156],"exactly":[157],"corresponding":[163],"norm":[165],"as":[166],"predicted.":[167]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
