{"id":"https://openalex.org/W1518534938","doi":"https://doi.org/10.1137/13094815x","title":"Finite Element Discretization Error Analysis of a General Interfacial Stress Functional","display_name":"Finite Element Discretization Error Analysis of a General Interfacial Stress Functional","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1518534938","doi":"https://doi.org/10.1137/13094815x","mag":"1518534938"},"language":"en","primary_location":{"id":"doi:10.1137/13094815x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/13094815x","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/A5060544465","display_name":"J\u00f6rg Grande","orcid":null},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"J\u00f6rg Grande","raw_affiliation_strings":["[Rwth Aachen University]"],"affiliations":[{"raw_affiliation_string":"[Rwth Aachen University]","institution_ids":["https://openalex.org/I887968799"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060544465"],"corresponding_institution_ids":["https://openalex.org/I887968799"],"apc_list":null,"apc_paid":null,"fwci":2.0062,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.84276424,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"53","issue":"3","first_page":"1236","last_page":"1255"},"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9980999827384949,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9860000014305115,"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/discretization","display_name":"Discretization","score":0.8844626545906067},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7237632870674133},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7072116136550903},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5487887263298035},{"id":"https://openalex.org/keywords/discretization-error","display_name":"Discretization error","score":0.53275465965271},{"id":"https://openalex.org/keywords/cauchy-stress-tensor","display_name":"Cauchy stress tensor","score":0.5244712829589844},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5084553956985474},{"id":"https://openalex.org/keywords/surface-tension","display_name":"Surface tension","score":0.4447348117828369},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4129420816898346},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23873090744018555},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1789878010749817},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07740381360054016}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8844626545906067},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7237632870674133},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7072116136550903},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5487887263298035},{"id":"https://openalex.org/C126148662","wikidata":"https://www.wikidata.org/wiki/Q3890355","display_name":"Discretization error","level":3,"score":0.53275465965271},{"id":"https://openalex.org/C171338203","wikidata":"https://www.wikidata.org/wiki/Q13409892","display_name":"Cauchy stress tensor","level":2,"score":0.5244712829589844},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5084553956985474},{"id":"https://openalex.org/C8892853","wikidata":"https://www.wikidata.org/wiki/Q170749","display_name":"Surface tension","level":2,"score":0.4447348117828369},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4129420816898346},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23873090744018555},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1789878010749817},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07740381360054016},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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":3,"locations":[{"id":"doi:10.1137/13094815x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/13094815x","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"},{"id":"pmh:oai:publications.rwth-aachen.de:229992","is_oa":false,"landing_page_url":"https://publications.rwth-aachen.de/record/229992","pdf_url":null,"source":{"id":"https://openalex.org/S4306401362","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Aachen : Institut f\u00fcr Geometrie und Praktische Mathematik, Bericht / Institut f\u00fcr Geometrie und Praktische Mathematik, RWTH Aachen 380, 19 S. (2014).","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:publications.rwth-aachen.de:659791","is_oa":false,"landing_page_url":"https://publications.rwth-aachen.de/record/659791","pdf_url":null,"source":{"id":"https://openalex.org/S4306401362","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM journal on numerical analysis 53(3), 1236-1255 (2015). doi:10.1137/13094815X","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1522020530","https://openalex.org/W1557324374","https://openalex.org/W1663357608","https://openalex.org/W1980964769","https://openalex.org/W1985270853","https://openalex.org/W1986113254","https://openalex.org/W1987954968","https://openalex.org/W1994672871","https://openalex.org/W1999510861","https://openalex.org/W2000537156","https://openalex.org/W2004588896","https://openalex.org/W2025022953","https://openalex.org/W2030119637","https://openalex.org/W2043377185","https://openalex.org/W2044892973","https://openalex.org/W2046237962","https://openalex.org/W2055009689","https://openalex.org/W2063974361","https://openalex.org/W2079259475","https://openalex.org/W2087240734","https://openalex.org/W2095006601","https://openalex.org/W2103155453","https://openalex.org/W2103309960","https://openalex.org/W2110649199","https://openalex.org/W2124614417","https://openalex.org/W2127368106","https://openalex.org/W2151306679","https://openalex.org/W2156149588","https://openalex.org/W2157670588","https://openalex.org/W2582902836","https://openalex.org/W2610428191","https://openalex.org/W3022173453"],"related_works":["https://openalex.org/W37066597","https://openalex.org/W25733641","https://openalex.org/W1977553163","https://openalex.org/W1993570899","https://openalex.org/W1555094802","https://openalex.org/W4230197975","https://openalex.org/W188298612","https://openalex.org/W3128822846","https://openalex.org/W2028070877","https://openalex.org/W2046814020"],"abstract_inverted_index":{"The":[0,61,80,104],"finite":[1,51],"element":[2,52],"discretization":[3,53,62],"of":[4,54,70,76,102],"a":[5,19,41,92],"variable":[6,13],"interfacial":[7,14,36,88],"stress":[8,37,89],"tensor":[9],"${\\sigma}^{\\Gamma}(x)$":[10],"is":[11,16,44,57,83,99,106],"considered;":[12],"tension":[15],"included":[17],"as":[18],"special":[20],"case.":[21],"Interfacial":[22],"stress,":[23],"for":[24,67,86],"example,":[25],"occurs":[26],"in":[27,91,111],"two-phase":[28],"flow":[29,78],"problems.":[30],"In":[31],"the":[32,35,47,68,71,74,77,87,96],"weak":[33],"formulation,":[34],"gives":[38],"rise":[39],"to":[40,108],"functional":[42,56,90],"which":[43],"supported":[45],"on":[46],"interface":[48,72,98],"$\\Gamma$.":[49,103],"A":[50],"this":[55],"presented":[58],"and":[59,73],"analyzed.":[60],"admits":[63],"almost":[64],"independent":[65],"meshes":[66],"approximation":[69,75],"variables.":[79],"main":[81],"result":[82],"an":[84,100],"$\\mathcal{O}(h^{k+1/2})$-error-bound":[85],"natural":[93],"norm":[94],"if":[95],"discrete":[97],"$\\mathcal{O}(h^{k+1})$-approximation":[101],"bound":[105],"shown":[107],"be":[109],"sharp":[110],"numerical":[112],"experiments.":[113]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
