The nonconforming virtual element method
We introduce the nonconforming Virtual Element Method (VEM) for the approximation of second order elliptic problems. We present the construction of the new element in two and three dimensions, highlighting the main differences with the conforming VEM and the classical nonconforming finite element me...
Gespeichert in:
| Veröffentlicht in: | ESAIM. Mathematical modelling and numerical analysis 2016-05, Vol.50 (3), p.879-904 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 904 |
|---|---|
| container_issue | 3 |
| container_start_page | 879 |
| container_title | ESAIM. Mathematical modelling and numerical analysis |
| container_volume | 50 |
| creator | Ayuso de Dios, Blanca Lipnikov, Konstantin Manzini, Gianmarco |
| description | We introduce the nonconforming Virtual Element Method (VEM) for the approximation of second order elliptic problems. We present the construction of the new element in two and three dimensions, highlighting the main differences with the conforming VEM and the classical nonconforming finite element methods. We provide the error analysis and establish the equivalence with a family of mimetic finite difference methods. Numerical experiments verify the theory and validate the performance of the proposed method. |
| doi_str_mv | 10.1051/m2an/2015090 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2199299524</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2199299524</sourcerecordid><originalsourceid>FETCH-LOGICAL-c339t-c09e022b0e2f6664cc11404623ae9750a612eabd300ff76607a16ba138f7100b3</originalsourceid><addsrcrecordid>eNo90EtPAjEUhuHGaCKiO3_AJG5cOHJOr9OlELxi3GB013SGVgaZKbaD0X8vBOLqbJ6cL3kJOUe4RhA4aKhtBxRQgIYD0kOqIWcFx0PSAyV5Lgr2fkxOUloAAAIXPXI5nbusDW0VWh9iU7cf2Xcdu7VdZm7pGtd2WeO6eZidkiNvl8md7W-fvN6Op6P7fPJy9zC6meQVY7rLK9AOKC3BUS-l5FWFyIFLyqzTSoCVSJ0tZwzAeyUlKIuytMgKrxCgZH1ysfu7iuFr7VJnFmEd282koag11VpQvlFXO1XFkFJ03qxi3dj4axDMtoXZtjD7Fhue73idOvfzb238NFIxJUwBb4YOH59RD8E8sT-R_l6B</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2199299524</pqid></control><display><type>article</type><title>The nonconforming virtual element method</title><source>Alma/SFX Local Collection</source><creator>Ayuso de Dios, Blanca ; Lipnikov, Konstantin ; Manzini, Gianmarco</creator><creatorcontrib>Ayuso de Dios, Blanca ; Lipnikov, Konstantin ; Manzini, Gianmarco</creatorcontrib><description>We introduce the nonconforming Virtual Element Method (VEM) for the approximation of second order elliptic problems. We present the construction of the new element in two and three dimensions, highlighting the main differences with the conforming VEM and the classical nonconforming finite element methods. We provide the error analysis and establish the equivalence with a family of mimetic finite difference methods. Numerical experiments verify the theory and validate the performance of the proposed method.</description><identifier>ISSN: 0764-583X</identifier><identifier>EISSN: 1290-3841</identifier><identifier>DOI: 10.1051/m2an/2015090</identifier><language>eng</language><publisher>Les Ulis: EDP Sciences</publisher><subject>65G99 ; 65N12 ; 65N30 ; 76R99 ; elliptic problems ; Error analysis ; Finite difference method ; Finite element method ; Mathematical analysis ; nonconforming method ; Nonlinear programming ; Numerical methods ; Poisson equation ; unstructured meshes ; Virtual element method</subject><ispartof>ESAIM. Mathematical modelling and numerical analysis, 2016-05, Vol.50 (3), p.879-904</ispartof><rights>2016. Notwithstanding the ProQuest Terms and conditions, you may use this content in accordance with the associated terms available at https://www.esaim-m2an.org/articles/m2an/abs/2016/03/m2an150085/m2an150085.html .</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c339t-c09e022b0e2f6664cc11404623ae9750a612eabd300ff76607a16ba138f7100b3</citedby><cites>FETCH-LOGICAL-c339t-c09e022b0e2f6664cc11404623ae9750a612eabd300ff76607a16ba138f7100b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,778,782,27907,27908</link.rule.ids></links><search><creatorcontrib>Ayuso de Dios, Blanca</creatorcontrib><creatorcontrib>Lipnikov, Konstantin</creatorcontrib><creatorcontrib>Manzini, Gianmarco</creatorcontrib><title>The nonconforming virtual element method</title><title>ESAIM. Mathematical modelling and numerical analysis</title><description>We introduce the nonconforming Virtual Element Method (VEM) for the approximation of second order elliptic problems. We present the construction of the new element in two and three dimensions, highlighting the main differences with the conforming VEM and the classical nonconforming finite element methods. We provide the error analysis and establish the equivalence with a family of mimetic finite difference methods. Numerical experiments verify the theory and validate the performance of the proposed method.</description><subject>65G99</subject><subject>65N12</subject><subject>65N30</subject><subject>76R99</subject><subject>elliptic problems</subject><subject>Error analysis</subject><subject>Finite difference method</subject><subject>Finite element method</subject><subject>Mathematical analysis</subject><subject>nonconforming method</subject><subject>Nonlinear programming</subject><subject>Numerical methods</subject><subject>Poisson equation</subject><subject>unstructured meshes</subject><subject>Virtual element method</subject><issn>0764-583X</issn><issn>1290-3841</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNo90EtPAjEUhuHGaCKiO3_AJG5cOHJOr9OlELxi3GB013SGVgaZKbaD0X8vBOLqbJ6cL3kJOUe4RhA4aKhtBxRQgIYD0kOqIWcFx0PSAyV5Lgr2fkxOUloAAAIXPXI5nbusDW0VWh9iU7cf2Xcdu7VdZm7pGtd2WeO6eZidkiNvl8md7W-fvN6Op6P7fPJy9zC6meQVY7rLK9AOKC3BUS-l5FWFyIFLyqzTSoCVSJ0tZwzAeyUlKIuytMgKrxCgZH1ysfu7iuFr7VJnFmEd282koag11VpQvlFXO1XFkFJ03qxi3dj4axDMtoXZtjD7Fhue73idOvfzb238NFIxJUwBb4YOH59RD8E8sT-R_l6B</recordid><startdate>201605</startdate><enddate>201605</enddate><creator>Ayuso de Dios, Blanca</creator><creator>Lipnikov, Konstantin</creator><creator>Manzini, Gianmarco</creator><general>EDP Sciences</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>201605</creationdate><title>The nonconforming virtual element method</title><author>Ayuso de Dios, Blanca ; Lipnikov, Konstantin ; Manzini, Gianmarco</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c339t-c09e022b0e2f6664cc11404623ae9750a612eabd300ff76607a16ba138f7100b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>65G99</topic><topic>65N12</topic><topic>65N30</topic><topic>76R99</topic><topic>elliptic problems</topic><topic>Error analysis</topic><topic>Finite difference method</topic><topic>Finite element method</topic><topic>Mathematical analysis</topic><topic>nonconforming method</topic><topic>Nonlinear programming</topic><topic>Numerical methods</topic><topic>Poisson equation</topic><topic>unstructured meshes</topic><topic>Virtual element method</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ayuso de Dios, Blanca</creatorcontrib><creatorcontrib>Lipnikov, Konstantin</creatorcontrib><creatorcontrib>Manzini, Gianmarco</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>ESAIM. Mathematical modelling and numerical analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ayuso de Dios, Blanca</au><au>Lipnikov, Konstantin</au><au>Manzini, Gianmarco</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The nonconforming virtual element method</atitle><jtitle>ESAIM. Mathematical modelling and numerical analysis</jtitle><date>2016-05</date><risdate>2016</risdate><volume>50</volume><issue>3</issue><spage>879</spage><epage>904</epage><pages>879-904</pages><issn>0764-583X</issn><eissn>1290-3841</eissn><abstract>We introduce the nonconforming Virtual Element Method (VEM) for the approximation of second order elliptic problems. We present the construction of the new element in two and three dimensions, highlighting the main differences with the conforming VEM and the classical nonconforming finite element methods. We provide the error analysis and establish the equivalence with a family of mimetic finite difference methods. Numerical experiments verify the theory and validate the performance of the proposed method.</abstract><cop>Les Ulis</cop><pub>EDP Sciences</pub><doi>10.1051/m2an/2015090</doi><tpages>26</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0764-583X |
| ispartof | ESAIM. Mathematical modelling and numerical analysis, 2016-05, Vol.50 (3), p.879-904 |
| issn | 0764-583X 1290-3841 |
| language | eng |
| recordid | cdi_proquest_journals_2199299524 |
| source | Alma/SFX Local Collection |
| subjects | 65G99 65N12 65N30 76R99 elliptic problems Error analysis Finite difference method Finite element method Mathematical analysis nonconforming method Nonlinear programming Numerical methods Poisson equation unstructured meshes Virtual element method |
| title | The nonconforming virtual element method |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-16T16%3A18%3A14IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20nonconforming%20virtual%20element%20method&rft.jtitle=ESAIM.%20Mathematical%20modelling%20and%20numerical%20analysis&rft.au=Ayuso%20de%20Dios,%20Blanca&rft.date=2016-05&rft.volume=50&rft.issue=3&rft.spage=879&rft.epage=904&rft.pages=879-904&rft.issn=0764-583X&rft.eissn=1290-3841&rft_id=info:doi/10.1051/m2an/2015090&rft_dat=%3Cproquest_cross%3E2199299524%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2199299524&rft_id=info:pmid/&rfr_iscdi=true |