{"id":"https://openalex.org/W2030028670","doi":"https://doi.org/10.1137/s0036142903432930","title":"<i>hp</i>-Interpolation of Nonsmooth Functions and an Application to<i>hp</i>-A posteriori Error Estimation","display_name":"<i>hp</i>-Interpolation of Nonsmooth Functions and an Application to<i>hp</i>-A posteriori Error Estimation","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2030028670","doi":"https://doi.org/10.1137/s0036142903432930","mag":"2030028670"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142903432930","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903432930","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/A5058356670","display_name":"Jens Markus Melenk","orcid":"https://orcid.org/0000-0001-9024-6028"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"J. M. Melenk","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058356670"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.1247,"has_fulltext":false,"cited_by_count":97,"citation_normalized_percentile":{"value":0.95887359,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"43","issue":"1","first_page":"127","last_page":"155"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9998000264167786,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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":0.8643693923950195},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7280390858650208},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.7145016193389893},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6979212760925293},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.659697413444519},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6346388459205627},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5549013018608093},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5165594816207886},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.46045947074890137},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29510095715522766},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21834644675254822},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12178516387939453},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10996970534324646},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08165594935417175}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8643693923950195},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7280390858650208},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.7145016193389893},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6979212760925293},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.659697413444519},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6346388459205627},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5549013018608093},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5165594816207886},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.46045947074890137},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29510095715522766},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21834644675254822},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12178516387939453},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10996970534324646},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08165594935417175},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142903432930","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903432930","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":33,"referenced_works":["https://openalex.org/W94458352","https://openalex.org/W1488877410","https://openalex.org/W1492326914","https://openalex.org/W1586623601","https://openalex.org/W1969923739","https://openalex.org/W1971878849","https://openalex.org/W1982739053","https://openalex.org/W1989248758","https://openalex.org/W1990941154","https://openalex.org/W1995404822","https://openalex.org/W1995613081","https://openalex.org/W2000450704","https://openalex.org/W2009985306","https://openalex.org/W2014077116","https://openalex.org/W2018383251","https://openalex.org/W2041586429","https://openalex.org/W2042112576","https://openalex.org/W2045737730","https://openalex.org/W2051043245","https://openalex.org/W2056040698","https://openalex.org/W2071036364","https://openalex.org/W2072744569","https://openalex.org/W2076074132","https://openalex.org/W2092011174","https://openalex.org/W2148903532","https://openalex.org/W2157121531","https://openalex.org/W2163679815","https://openalex.org/W2199169705","https://openalex.org/W2307113332","https://openalex.org/W2505585705","https://openalex.org/W2566563028","https://openalex.org/W4205354563","https://openalex.org/W4292166829"],"related_works":["https://openalex.org/W4388311650","https://openalex.org/W5922282","https://openalex.org/W2560215812","https://openalex.org/W1974056099","https://openalex.org/W4245343541","https://openalex.org/W2386077341","https://openalex.org/W563589758","https://openalex.org/W62490179","https://openalex.org/W2954004777","https://openalex.org/W2951102138"],"abstract_inverted_index":{"The":[0,27],"quasi-interpolation":[1],"operators":[2],"of":[3,13],"Cl\u00e9ment":[4],"and":[5,22],"Scott--Zhang":[6],"type":[7],"are":[8,25],"generalized":[9,36],"to":[10,37],"the":[11,14,38],"setting":[12],"hp-FEM":[15],"(finite":[16],"element":[17],"method).":[18],"New":[19],"polynomial":[20],"lifting":[21],"inverse":[23],"estimates":[24],"presented.":[26],"classical":[28],"residual":[29],"based":[30],"a":[31],"posteriori":[32],"error":[33],"estimator":[34],"is":[35],"hp-FEM.":[39]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}