{"id":"https://openalex.org/W2004588896","doi":"https://doi.org/10.1137/060667530","title":"Finite Element Discretization Error Analysis of a Surface Tension Force in Two-Phase Incompressible Flows","display_name":"Finite Element Discretization Error Analysis of a Surface Tension Force in Two-Phase Incompressible Flows","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2004588896","doi":"https://doi.org/10.1137/060667530","mag":"2004588896"},"language":"en","primary_location":{"id":"doi:10.1137/060667530","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060667530","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/A5005631647","display_name":"Sven Gro\u00df","orcid":"https://orcid.org/0000-0002-6968-4258"},"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":"Sven Gross","raw_affiliation_strings":["[Rwth Aachen University]"],"affiliations":[{"raw_affiliation_string":"[Rwth Aachen University]","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109253345","display_name":"Arnold Reusken","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Arnold Reusken","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5005631647"],"corresponding_institution_ids":["https://openalex.org/I887968799"],"apc_list":null,"apc_paid":null,"fwci":6.8555,"has_fulltext":false,"cited_by_count":68,"citation_normalized_percentile":{"value":0.96981935,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"45","issue":"4","first_page":"1679","last_page":"1700"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9977999925613403,"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":0.7882993817329407},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7515630722045898},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6608248353004456},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.629116415977478},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5755137205123901},{"id":"https://openalex.org/keywords/surface-tension","display_name":"Surface tension","score":0.5518666505813599},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.49371108412742615},{"id":"https://openalex.org/keywords/incompressible-flow","display_name":"Incompressible flow","score":0.49058499932289124},{"id":"https://openalex.org/keywords/mean-curvature","display_name":"Mean curvature","score":0.4408486485481262},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.41515401005744934},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.34940874576568604},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.28301870822906494},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.20291617512702942},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14196869730949402}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7882993817329407},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7515630722045898},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6608248353004456},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.629116415977478},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5755137205123901},{"id":"https://openalex.org/C8892853","wikidata":"https://www.wikidata.org/wiki/Q170749","display_name":"Surface tension","level":2,"score":0.5518666505813599},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.49371108412742615},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.49058499932289124},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.4408486485481262},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.41515401005744934},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.34940874576568604},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.28301870822906494},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.20291617512702942},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14196869730949402},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/060667530","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060667530","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:CiteSeerX.psu:10.1.1.148.8106","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.148.8106","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.igpm.rwth-aachen.de/Download/reports/pdf/IGPM262.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.514.2830","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.514.2830","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.igpm.rwth-aachen.de/Download/reports/reusken/ARpaper41.pdf","raw_type":"text"},{"id":"pmh:oai:publications.rwth-aachen.de:158508","is_oa":false,"landing_page_url":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-036748%22","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 45(4), 1679-1700 (2007). doi:10.1137/060667530","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:publications.rwth-aachen.de:47204","is_oa":false,"landing_page_url":"https://publications.rwth-aachen.de/record/47204","pdf_url":null,"source":{"id":"https://openalex.org/S4306401033","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 262, 21 S. (2006).","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":28,"referenced_works":["https://openalex.org/W116250134","https://openalex.org/W1564993852","https://openalex.org/W1578207426","https://openalex.org/W1674659126","https://openalex.org/W1977402577","https://openalex.org/W1980440487","https://openalex.org/W1994875376","https://openalex.org/W2001254200","https://openalex.org/W2016447000","https://openalex.org/W2024876823","https://openalex.org/W2029190578","https://openalex.org/W2030119637","https://openalex.org/W2045545335","https://openalex.org/W2046237962","https://openalex.org/W2049465597","https://openalex.org/W2058981386","https://openalex.org/W2062832849","https://openalex.org/W2063974361","https://openalex.org/W2080922987","https://openalex.org/W2103309960","https://openalex.org/W2108745988","https://openalex.org/W2119692497","https://openalex.org/W2120261090","https://openalex.org/W2123048683","https://openalex.org/W2149053014","https://openalex.org/W2154121625","https://openalex.org/W2998023265","https://openalex.org/W3020850290"],"related_works":["https://openalex.org/W4244718299","https://openalex.org/W2012983134","https://openalex.org/W4388599312","https://openalex.org/W86477321","https://openalex.org/W2131115966","https://openalex.org/W1669816071","https://openalex.org/W2039262714","https://openalex.org/W2093607043","https://openalex.org/W2743552406","https://openalex.org/W4231453159"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,6,21,44,61,81],"standard":[3],"model":[4,20],"for":[5,71],"stationary":[7],"two-phase":[8],"incompressible":[9],"flow":[10],"with":[11,80],"surface":[12,27],"tension.":[13],"In":[14,43],"the":[15,19,26,35,38,41,49,65,72],"variational":[16],"formulation":[17],"of":[18,40,64],"linear":[22],"functional":[23,32,50],"which":[24],"describes":[25],"tension":[28],"force":[29],"occurs.":[30],"This":[31],"depends":[33],"on":[34,60],"location":[36],"and":[37],"curvature":[39,66],"interface.":[42],"finite":[45],"element":[46],"discretization":[47],"method":[48,58,79],"has":[51],"to":[52],"be":[53],"approximated.":[54],"For":[55],"an":[56],"approximation":[57,73,78],"based":[59],"Laplace\u2013Beltrami":[62],"representation":[63],"we":[67],"derive":[68],"sharp":[69],"bounds":[70],"error.":[74],"A":[75],"new":[76],"modified":[77],"significantly":[82],"smaller":[83],"error":[84],"is":[85],"introduced.":[86]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}