{"id":"https://openalex.org/W1981581845","doi":"https://doi.org/10.1137/060666524","title":"Local Anisotropic Interpolation Error Estimates Based on Directional Derivatives Along Edges","display_name":"Local Anisotropic Interpolation Error Estimates Based on Directional Derivatives Along Edges","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1981581845","doi":"https://doi.org/10.1137/060666524","mag":"1981581845"},"language":"en","primary_location":{"id":"doi:10.1137/060666524","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060666524","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/A5049981295","display_name":"Ulrich Hetmaniuk","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"U. Hetmaniuk","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5085988232","display_name":"Patrick Knupp","orcid":"https://orcid.org/0000-0003-4217-6787"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. Knupp","raw_affiliation_strings":["ulhetma@sandia.gov and pknupp@sandia.gov#TAB#"],"affiliations":[{"raw_affiliation_string":"ulhetma@sandia.gov and pknupp@sandia.gov#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5049981295"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9686,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.8433221,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"47","issue":"1","first_page":"575","last_page":"595"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9997000098228455,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9991999864578247,"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":0.9961000084877014,"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/mathematics","display_name":"Mathematics","score":0.7971842288970947},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.7158557772636414},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5988577604293823},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5001034736633301},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.46870869398117065},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4673460125923157},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4421965777873993},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3813183307647705},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3514471650123596},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0765751302242279},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.06636166572570801}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7971842288970947},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.7158557772636414},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5988577604293823},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5001034736633301},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.46870869398117065},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4673460125923157},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4421965777873993},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3813183307647705},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3514471650123596},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0765751302242279},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.06636166572570801},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/060666524","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060666524","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1573835018","https://openalex.org/W1973071447","https://openalex.org/W1979518155","https://openalex.org/W2012229545","https://openalex.org/W2030982479","https://openalex.org/W2038596716","https://openalex.org/W2062599983","https://openalex.org/W2069426867","https://openalex.org/W2071415238","https://openalex.org/W2082130386","https://openalex.org/W2142693250","https://openalex.org/W2171737318","https://openalex.org/W2934526567"],"related_works":["https://openalex.org/W2038416447","https://openalex.org/W2364151838","https://openalex.org/W2055836843","https://openalex.org/W2755775996","https://openalex.org/W2066926363","https://openalex.org/W2354159744","https://openalex.org/W2773728674","https://openalex.org/W2069701013","https://openalex.org/W2351539857","https://openalex.org/W2366062865"],"abstract_inverted_index":{"We":[0],"present":[1],"new":[2,38,63,72,94],"local":[3],"anisotropic":[4],"error":[5,107],"estimates":[6],"for":[7],"the":[8,27,53,62,67,71,77,80,97,102,105,114],"Lagrangian":[9],"finite":[10],"element":[11,81],"interpolation.":[12],"The":[13],"bounds":[14,39,75],"apply":[15],"to":[16,29,83],"affine":[17],"equivalent":[18],"elements":[19,87],"and":[20,73],"use":[21],"information":[22],"from":[23,61],"directional":[24],"derivatives":[25],"of":[26,34,70,79,104],"function":[28],"interpolate":[30],"along":[31],"a":[32],"set":[33],"adjacent":[35],"edges.":[36],"These":[37],"do":[40,111],"not":[41,112],"require":[42],"any":[43],"geometric":[44],"limitation":[45],"but":[46],"may":[47],"vary,":[48],"in":[49],"some":[50,86],"cases,":[51],"with":[52,88],"node":[54],"ordering.":[55],"Several":[56],"existing":[57,74,109],"results":[58,110],"are":[59],"recovered":[60],"bounds.":[64],"Examples":[65],"compare":[66],"asymptotic":[68,99,116],"behavior":[69,100],"when":[76],"diameter":[78],"goes":[82],"zero.":[84],"For":[85],"small":[89],"or":[90],"large":[91],"angles,":[92],"our":[93],"bound":[95],"exhibits":[96],"same":[98],"as":[101],"norm":[103],"interpolation":[106],"while":[108],"have":[113],"correct":[115],"behavior.":[117]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
