{"id":"https://openalex.org/W2009259073","doi":"https://doi.org/10.1137/050639387","title":"Mathematical and Numerical Analysis of a Robust and Efficient Grid Deformation Method in the Finite Element Context","display_name":"Mathematical and Numerical Analysis of a Robust and Efficient Grid Deformation Method in the Finite Element Context","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2009259073","doi":"https://doi.org/10.1137/050639387","mag":"2009259073"},"language":"en","primary_location":{"id":"doi:10.1137/050639387","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050639387","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5088024316","display_name":"Matthias Grajewski","orcid":null},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Matthias Grajewski","raw_affiliation_strings":["matthias.grajewski@mathematik.tu-dortmund.de and michael.koester@mathematik.tu-dortmund.de and ture@featflow.de#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"matthias.grajewski@mathematik.tu-dortmund.de and michael.koester@mathematik.tu-dortmund.de and ture@featflow.de#TAB#","institution_ids":["https://openalex.org/I200332995"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045296981","display_name":"M. K\u00f6ster","orcid":"https://orcid.org/0000-0002-1729-1591"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael K\u00f6ster","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5059837563","display_name":"Stefan Turek","orcid":"https://orcid.org/0000-0002-9740-6087"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stefan Turek","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.4711,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.92646882,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"31","issue":"2","first_page":"1539","last_page":"1557"},"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":0.9998000264167786,"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"}},"topics":[{"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9983999729156494,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7136152386665344},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.688103199005127},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6663188934326172},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5839765071868896},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.568278431892395},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5316475033760071},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5162677764892578},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4788375198841095},{"id":"https://openalex.org/keywords/mesh-generation","display_name":"Mesh generation","score":0.4752908945083618},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.43647730350494385},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3023122549057007},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2212032973766327}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7136152386665344},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.688103199005127},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6663188934326172},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5839765071868896},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.568278431892395},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5316475033760071},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5162677764892578},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4788375198841095},{"id":"https://openalex.org/C181145010","wikidata":"https://www.wikidata.org/wiki/Q4418033","display_name":"Mesh generation","level":3,"score":0.4752908945083618},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.43647730350494385},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3023122549057007},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2212032973766327},{"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050639387","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050639387","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.712.7759","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.712.7759","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathematik.tu-dortmund.de/lsiii/cms/papers/GrajewskiKoesterTurek2008.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W75801351","https://openalex.org/W1964753390","https://openalex.org/W1979639437","https://openalex.org/W1981849590","https://openalex.org/W1987022010","https://openalex.org/W1993974670","https://openalex.org/W2003419577","https://openalex.org/W2018405441","https://openalex.org/W2028949045","https://openalex.org/W2043661645","https://openalex.org/W2059102113","https://openalex.org/W2069426867","https://openalex.org/W2079292872","https://openalex.org/W2097566513","https://openalex.org/W2111835916","https://openalex.org/W2137674306","https://openalex.org/W2167796170","https://openalex.org/W4244258518","https://openalex.org/W4252628010"],"related_works":["https://openalex.org/W1517908938","https://openalex.org/W2281834912","https://openalex.org/W1489941249","https://openalex.org/W3123492739","https://openalex.org/W4320486059","https://openalex.org/W2494168571","https://openalex.org/W3121191496","https://openalex.org/W1550676882","https://openalex.org/W2349419863","https://openalex.org/W1485433551"],"abstract_inverted_index":{"Among":[0],"a":[1,70,74,103,112],"variety":[2],"of":[3,47,76,91,105,137],"grid":[4],"deformation":[5,84],"methods,":[6,85],"the":[7,48,61,89,135],"method":[8],"proposed":[9],"by":[10,144],"Bochev,":[11],"Liao,":[12],"and":[13,35,37,56,73,133],"de":[14],"la":[15],"Pena":[16],"[Methods":[17],"Partial":[18],"Differential":[19],"Equations,":[20],"12":[21],"(1996),":[22],"pp.":[23,33,43],"489\u2013506],":[24],"Cai":[25],"et":[26],"al.":[27],"[Comput.":[28],"Math.":[29],"Appl.,":[30],"48":[31],"(2004),":[32],"1077\u20131086],":[34],"Liao":[36],"Anderson":[38],"[Appl.":[39],"Anal.,":[40],"44":[41],"(1992),":[42],"285\u2013298]":[44],"is":[45],"one":[46],"most":[49],"favorable,":[50],"because":[51],"it":[52],"prevents":[53],"mesh":[54,114,125],"tangling":[55],"offers":[57],"precise":[58],"control":[59],"over":[60],"element":[62],"volumes.":[63],"Its":[64],"numerical":[65,131,145],"realization":[66,132],"requires":[67],"only":[68],"solving":[69],"Poisson":[71],"problem":[72],"system":[75],"fully":[77],"decoupled":[78],"initial":[79],"value":[80],"problems.":[81],"Many":[82],"other":[83],"in":[86],"contrast,":[87],"involve":[88],"solution":[90],"complicated":[92],"nonlinear":[93],"partial":[94],"differential":[95],"equations":[96],"(PDEs).":[97],"In":[98],"this":[99],"article,":[100],"we":[101],"introduce":[102],"generalization":[104],"Liao's":[106],"method,":[107],"which":[108],"allows":[109],"for":[110,117],"generating":[111],"desired":[113],"size":[115],"distribution":[116],"quite":[118],"arbitrary":[119],"grids":[120],"without":[121],"giving":[122],"rise":[123],"to":[124],"tangling.":[126],"We":[127],"elaborate":[128],"on":[129],"its":[130],"prove":[134],"convergence":[136],"our":[138],"method.":[139],"Our":[140],"results":[141],"are":[142],"confirmed":[143],"experiments.":[146]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}