{"id":"https://openalex.org/W2157670588","doi":"https://doi.org/10.1017/s0962492913000056","title":"Finite element methods for surface PDEs","display_name":"Finite element methods for surface PDEs","publication_year":2013,"publication_date":"2013-04-02","ids":{"openalex":"https://openalex.org/W2157670588","doi":"https://doi.org/10.1017/s0962492913000056","mag":"2157670588"},"language":"en","primary_location":{"id":"doi:10.1017/s0962492913000056","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0962492913000056","pdf_url":null,"source":{"id":"https://openalex.org/S124973578","display_name":"Acta Numerica","issn_l":"0962-4929","issn":["0962-4929","1474-0508"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Numerica","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/A5089965962","display_name":"Gerhard Dziuk","orcid":null},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gerhard Dziuk","raw_affiliation_strings":["Abteilung f\u00fcr Angewandte Mathematik, Albert-Ludwigs-Universit\u00e4t Freiburg im Breisgau, Hermann-Herder-Stra\u03b2e 10, D\u201379104 Freiburg im Breisgau, Germany E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Abteilung f\u00fcr Angewandte Mathematik, Albert-Ludwigs-Universit\u00e4t Freiburg im Breisgau, Hermann-Herder-Stra\u03b2e 10, D\u201379104 Freiburg im Breisgau, Germany E-mail:","institution_ids":["https://openalex.org/I161046081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027234006","display_name":"Charles M. Elliott","orcid":"https://orcid.org/0000-0002-6924-4455"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Charles M. Elliott","raw_affiliation_strings":["Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK E-mail:","institution_ids":["https://openalex.org/I39555362"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":41.6239,"has_fulltext":false,"cited_by_count":647,"citation_normalized_percentile":{"value":0.99936285,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"22","issue":null,"first_page":"289","last_page":"396"},"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":0.9993000030517578,"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/T10514","display_name":"Numerical methods in engineering","score":0.9959999918937683,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7706595063209534},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.6192489266395569},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.609043300151825},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5789708495140076},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5305607318878174},{"id":"https://openalex.org/keywords/extended-finite-element-method","display_name":"Extended finite element method","score":0.5182626247406006},{"id":"https://openalex.org/keywords/numerical-partial-differential-equations","display_name":"Numerical partial differential equations","score":0.5111678242683411},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4872945547103882},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.4831511378288269},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.4639633893966675},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.462867796421051},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4591895639896393},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43642500042915344},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32367396354675293},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28056132793426514},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.25057703256607056},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11391124129295349},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06781861186027527},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.05436322093009949}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7706595063209534},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.6192489266395569},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.609043300151825},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5789708495140076},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5305607318878174},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.5182626247406006},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.5111678242683411},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4872945547103882},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.4831511378288269},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.4639633893966675},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.462867796421051},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4591895639896393},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43642500042915344},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32367396354675293},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28056132793426514},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25057703256607056},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11391124129295349},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06781861186027527},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.05436322093009949},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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":2,"locations":[{"id":"doi:10.1017/s0962492913000056","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0962492913000056","pdf_url":null,"source":{"id":"https://openalex.org/S124973578","display_name":"Acta Numerica","issn_l":"0962-4929","issn":["0962-4929","1474-0508"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Numerica","raw_type":"journal-article"},{"id":"pmh:oai:wrap.warwick.ac.uk:53966","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","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":106,"referenced_works":["https://openalex.org/W50490584","https://openalex.org/W58623853","https://openalex.org/W138643006","https://openalex.org/W1504765007","https://openalex.org/W1518550563","https://openalex.org/W1536812363","https://openalex.org/W1866311589","https://openalex.org/W1883449737","https://openalex.org/W1965552352","https://openalex.org/W1968419084","https://openalex.org/W1969090524","https://openalex.org/W1970875985","https://openalex.org/W1979234362","https://openalex.org/W1980661496","https://openalex.org/W1981891092","https://openalex.org/W1984435110","https://openalex.org/W1991325491","https://openalex.org/W2000537156","https://openalex.org/W2001776082","https://openalex.org/W2002644597","https://openalex.org/W2003154163","https://openalex.org/W2003173073","https://openalex.org/W2005358459","https://openalex.org/W2006161819","https://openalex.org/W2008398287","https://openalex.org/W2009262561","https://openalex.org/W2009544619","https://openalex.org/W2010334793","https://openalex.org/W2016169380","https://openalex.org/W2021203048","https://openalex.org/W2021505562","https://openalex.org/W2022819931","https://openalex.org/W2023918388","https://openalex.org/W2024348166","https://openalex.org/W2024394198","https://openalex.org/W2029110113","https://openalex.org/W2029870529","https://openalex.org/W2033994983","https://openalex.org/W2037677028","https://openalex.org/W2038480876","https://openalex.org/W2040896717","https://openalex.org/W2041523977","https://openalex.org/W2043377185","https://openalex.org/W2043546299","https://openalex.org/W2048968266","https://openalex.org/W2050258527","https://openalex.org/W2051315259","https://openalex.org/W2051483974","https://openalex.org/W2052006012","https://openalex.org/W2052395157","https://openalex.org/W2053364845","https://openalex.org/W2055786818","https://openalex.org/W2056087726","https://openalex.org/W2058981386","https://openalex.org/W2061062939","https://openalex.org/W2063974361","https://openalex.org/W2064240269","https://openalex.org/W2065729312","https://openalex.org/W2066880755","https://openalex.org/W2071121523","https://openalex.org/W2075289636","https://openalex.org/W2075449639","https://openalex.org/W2076776678","https://openalex.org/W2079518959","https://openalex.org/W2083629653","https://openalex.org/W2089600426","https://openalex.org/W2091323047","https://openalex.org/W2091904688","https://openalex.org/W2092509712","https://openalex.org/W2093834886","https://openalex.org/W2094963146","https://openalex.org/W2102635728","https://openalex.org/W2103155453","https://openalex.org/W2106079716","https://openalex.org/W2111377429","https://openalex.org/W2113751265","https://openalex.org/W2115218270","https://openalex.org/W2115246370","https://openalex.org/W2115847587","https://openalex.org/W2117708954","https://openalex.org/W2117828664","https://openalex.org/W2123378618","https://openalex.org/W2123996636","https://openalex.org/W2125344654","https://openalex.org/W2134663418","https://openalex.org/W2137053032","https://openalex.org/W2138026128","https://openalex.org/W2144614420","https://openalex.org/W2149691830","https://openalex.org/W2151306679","https://openalex.org/W2153251956","https://openalex.org/W2156268854","https://openalex.org/W2167606637","https://openalex.org/W2291283624","https://openalex.org/W2998023265","https://openalex.org/W3021722416","https://openalex.org/W3100925412","https://openalex.org/W3103746622","https://openalex.org/W3104082195","https://openalex.org/W3200227310","https://openalex.org/W4245101459","https://openalex.org/W4386445991","https://openalex.org/W6632239630","https://openalex.org/W6642196336","https://openalex.org/W6676987805","https://openalex.org/W6801601058"],"related_works":["https://openalex.org/W1977906733","https://openalex.org/W1567939749","https://openalex.org/W2010821947","https://openalex.org/W4234008889","https://openalex.org/W1573186872","https://openalex.org/W2071722255","https://openalex.org/W2352023866","https://openalex.org/W2021654023","https://openalex.org/W2165887158","https://openalex.org/W2350569191"],"abstract_inverted_index":{"In":[0,45],"this":[1],"article":[2],"we":[3,51],"consider":[4],"finite":[5,22,38],"element":[6,39],"methods":[7,29,40,50],"for":[8],"approximating":[9],"the":[10,35,49,53,59,64,80],"solution":[11],"of":[12,34,61,71,79],"partial":[13],"differential":[14],"equations":[15,72],"on":[16,20,24],"surfaces.":[17],"We":[18],"focus":[19],"surface":[21,28],"elements":[23],"triangulated":[25],"surfaces,":[26,63],"implicit":[27],"using":[30],"level":[31],"set":[32],"descriptions":[33],"surface,":[36],"unfitted":[37],"and":[41,73],"diffuse":[42],"interface":[43],"methods.":[44],"order":[46],"to":[47],"formulate":[48],"present":[52],"necessary":[54,65],"geometric":[55],"analysis":[56,82],"and,":[57],"in":[58],"context":[60],"evolving":[62],"transport":[66],"formulae.":[67],"A":[68],"wide":[69],"variety":[70],"applications":[74],"are":[75,83],"covered.":[76],"Some":[77],"ideas":[78],"numerical":[81,88],"presented":[84],"along":[85],"with":[86],"illustrative":[87],"examples.":[89]},"counts_by_year":[{"year":2026,"cited_by_count":25},{"year":2025,"cited_by_count":59},{"year":2024,"cited_by_count":54},{"year":2023,"cited_by_count":67},{"year":2022,"cited_by_count":50},{"year":2021,"cited_by_count":57},{"year":2020,"cited_by_count":64},{"year":2019,"cited_by_count":52},{"year":2018,"cited_by_count":48},{"year":2017,"cited_by_count":52},{"year":2016,"cited_by_count":40},{"year":2015,"cited_by_count":50},{"year":2014,"cited_by_count":22},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}
