Stable cheapest nonconforming finite elements for the Stokes equations
We introduce two pairs of stable cheapest nonconforming finite element space pairs to approximate the Stokes equations. One pair has each component of its velocity field to be approximated by the P1 nonconforming quadrilateral element while the pressure field is approximated by the piecewise constan...
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| Veröffentlicht in: | Journal of computational and applied mathematics 2016-06, Vol.299, p.2-14 |
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| creator | Kim, Sihwan Yim, Jaeryun Sheen, Dongwoo |
| description | We introduce two pairs of stable cheapest nonconforming finite element space pairs to approximate the Stokes equations. One pair has each component of its velocity field to be approximated by the P1 nonconforming quadrilateral element while the pressure field is approximated by the piecewise constant function with globally two-dimensional subspaces removed: one removed space is due to the integral mean-zero property and the other space consists of global checker-board patterns. The other pair consists of the velocity space as the P1 nonconforming quadrilateral element enriched by a globally one-dimensional macro bubble function space based on DSSY (Douglas–Santos–Sheen–Ye) nonconforming finite element space; the pressure field is approximated by the piecewise constant function with mean-zero space eliminated. We show that two element pairs satisfy the discrete inf–sup condition uniformly. And we investigate the relationship between them. Several numerical examples are shown to confirm the efficiency and reliability of the proposed methods. |
| doi_str_mv | 10.1016/j.cam.2015.06.021 |
| format | Article |
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Several numerical examples are shown to confirm the efficiency and reliability of the proposed methods.</description><subject>Approximation</subject><subject>Constants</subject><subject>Finite element method</subject><subject>Fluid flow</subject><subject>Function space</subject><subject>Inf–sup condition</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Nonconforming finite element</subject><subject>Quadrilaterals</subject><subject>Stokes problem</subject><issn>0377-0427</issn><issn>1879-1778</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp9kLFOwzAQhi0EEqXwAGwZWRJ8cWwnYkIVBaRKDIXZSuwLdUns1naReHtSlZnppNP_nf77CLkFWgAFcb8tdDsWJQVeUFHQEs7IDGrZ5CBlfU5mlEmZ06qUl-Qqxi2lVDRQzchyndpuwExvsN1hTJnzTnvX-zBa95n11tmEGQ44oksxm_ZZ2mC2Tv4LY4b7Q5usd_GaXPTtEPHmb87Jx_LpffGSr96eXxePq1xXFUt5yQFQIjPImGFTS1kbqhkVLa-FKQUHzhhvGi5LrTtRctOBBGMazgR0YNic3J3u7oLfH6a-arRR4zC0Dv0hKpANKxsGUE1ROEV18DEG7NUu2LENPwqoOjpTWzU5U0dnigo1tZmYhxOD0w_fFoOK2qLTaGxAnZTx9h_6FwqBc2g</recordid><startdate>20160601</startdate><enddate>20160601</enddate><creator>Kim, Sihwan</creator><creator>Yim, Jaeryun</creator><creator>Sheen, Dongwoo</creator><general>Elsevier B.V</general><scope>6I.</scope><scope>AAFTH</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>20160601</creationdate><title>Stable cheapest nonconforming finite elements for the Stokes equations</title><author>Kim, Sihwan ; Yim, Jaeryun ; Sheen, Dongwoo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c443t-2511e7e3de33d302178d0c306a586d2651533599572ccb625db171dd95361b1d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Approximation</topic><topic>Constants</topic><topic>Finite element method</topic><topic>Fluid flow</topic><topic>Function space</topic><topic>Inf–sup condition</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Nonconforming finite element</topic><topic>Quadrilaterals</topic><topic>Stokes problem</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kim, Sihwan</creatorcontrib><creatorcontrib>Yim, Jaeryun</creatorcontrib><creatorcontrib>Sheen, Dongwoo</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</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>Journal of computational and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kim, Sihwan</au><au>Yim, Jaeryun</au><au>Sheen, Dongwoo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stable cheapest nonconforming finite elements for the Stokes equations</atitle><jtitle>Journal of computational and applied mathematics</jtitle><date>2016-06-01</date><risdate>2016</risdate><volume>299</volume><spage>2</spage><epage>14</epage><pages>2-14</pages><issn>0377-0427</issn><eissn>1879-1778</eissn><abstract>We introduce two pairs of stable cheapest nonconforming finite element space pairs to approximate the Stokes equations. 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| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Approximation Constants Finite element method Fluid flow Function space Inf–sup condition Mathematical analysis Mathematical models Nonconforming finite element Quadrilaterals Stokes problem |
| title | Stable cheapest nonconforming finite elements for the Stokes equations |
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