{"id":"https://openalex.org/W1969100313","doi":"https://doi.org/10.1007/s00211-004-0546-5","title":"Error analysis of a mixed finite element method for the Cahn-Hilliard equation","display_name":"Error analysis of a mixed finite element method for the Cahn-Hilliard equation","publication_year":2004,"publication_date":"2004-09-06","ids":{"openalex":"https://openalex.org/W1969100313","doi":"https://doi.org/10.1007/s00211-004-0546-5","mag":"1969100313"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-004-0546-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-004-0546-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-004-0546-5.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s00211-004-0546-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011365911","display_name":"Xiaobing Feng","orcid":"https://orcid.org/0000-0002-9191-9092"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Xiaobing Feng","raw_affiliation_strings":["Department of Mathematics, The University of Tennessee, Knoxville, TN, 37996, USA","The University of Tennessee, Department of Mathematics, 37996, Knoxville, TN, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Tennessee, Knoxville, TN, 37996, USA","institution_ids":["https://openalex.org/I75027704"]},{"raw_affiliation_string":"The University of Tennessee, Department of Mathematics, 37996, Knoxville, TN, USA#TAB#","institution_ids":["https://openalex.org/I75027704"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046668672","display_name":"Andreas Prohl","orcid":"https://orcid.org/0000-0003-4523-9536"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Andreas Prohl","raw_affiliation_strings":["Department of Mathematics, ETH Zurich, 8092, Zurich, Switzerland","ETH Zurich, Department of Mathematics, 8092, Zurich, TN, Switzerland#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, ETH Zurich, 8092, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"ETH Zurich, Department of Mathematics, 8092, Zurich, TN, Switzerland#TAB#","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5011365911"],"corresponding_institution_ids":["https://openalex.org/I75027704"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.9204,"has_fulltext":true,"cited_by_count":186,"citation_normalized_percentile":{"value":0.84333295,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"99","issue":"1","first_page":"47","last_page":"84"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9936000108718872,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9886999726295471,"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":0.8535046577453613},{"id":"https://openalex.org/keywords/cahn\u2013hilliard-equation","display_name":"Cahn\u2013Hilliard equation","score":0.75864577293396},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6978331804275513},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6106899380683899},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5796722769737244},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5001621246337891},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.49138227105140686},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4889144003391266},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.483418345451355},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4804939031600952},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4770050346851349},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.47104597091674805},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.44062793254852295},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.41333240270614624},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.19062131643295288},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0728941261768341}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8535046577453613},{"id":"https://openalex.org/C24822716","wikidata":"https://www.wikidata.org/wiki/Q5017440","display_name":"Cahn\u2013Hilliard equation","level":3,"score":0.75864577293396},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6978331804275513},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6106899380683899},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5796722769737244},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5001621246337891},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.49138227105140686},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4889144003391266},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.483418345451355},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4804939031600952},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4770050346851349},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.47104597091674805},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.44062793254852295},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.41333240270614624},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.19062131643295288},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0728941261768341},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00211-004-0546-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-004-0546-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-004-0546-5.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:doc.rero.ch:313134","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400148","display_name":"reroDoc Digital Library","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/38267","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/38267","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Numerische Mathematik, 99 (1)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"doi:10.3929/ethz-b-000038267","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000038267","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1007/s00211-004-0546-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-004-0546-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-004-0546-5.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1969100313.pdf","grobid_xml":"https://content.openalex.org/works/W1969100313.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W69091152","https://openalex.org/W1492326914","https://openalex.org/W1518792628","https://openalex.org/W1593414945","https://openalex.org/W1596838038","https://openalex.org/W1815006409","https://openalex.org/W1965753687","https://openalex.org/W1992445851","https://openalex.org/W2003173073","https://openalex.org/W2011723842","https://openalex.org/W2025245542","https://openalex.org/W2025739397","https://openalex.org/W2027777648","https://openalex.org/W2032257836","https://openalex.org/W2034879619","https://openalex.org/W2041001120","https://openalex.org/W2041523977","https://openalex.org/W2043140935","https://openalex.org/W2044417927","https://openalex.org/W2044562696","https://openalex.org/W2045823559","https://openalex.org/W2046528357","https://openalex.org/W2047626766","https://openalex.org/W2062245988","https://openalex.org/W2066625579","https://openalex.org/W2077028260","https://openalex.org/W2079028266","https://openalex.org/W2083629653","https://openalex.org/W2086238793","https://openalex.org/W2110176271","https://openalex.org/W2114612290","https://openalex.org/W2138026128","https://openalex.org/W2161508768","https://openalex.org/W2286857290","https://openalex.org/W2587075603","https://openalex.org/W2934526567","https://openalex.org/W4256064871","https://openalex.org/W4285719527","https://openalex.org/W4292166829"],"related_works":["https://openalex.org/W2967558384","https://openalex.org/W2048454885","https://openalex.org/W2077028260","https://openalex.org/W57680709","https://openalex.org/W2059693824","https://openalex.org/W1969464363","https://openalex.org/W2973230771","https://openalex.org/W4390682253","https://openalex.org/W4388722486","https://openalex.org/W2083629653"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":18},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":15},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":9}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}