Geodesic
Cubic Lagrange elements satisfying exact incompressibility
Guzmán, Johnny1 ; Scott, L. Ridgway2
1 Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
2 Departments of Computer Science and Mathematics, Committee on Computational and Applied Mathematics, University of Chicago, Chicago IL 60637, USA
The SMAI Journal of computational mathematics, Tome 4 (2018), pp. 345-374

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We prove that an analog of the Scott-Vogelius finite elements are inf-sup stable on certain nondegenerate meshes for piecewise cubic velocity fields. We also characterize the divergence of the velocity space on such meshes. In addition, we show how such a characterization relates to the dimension of C 1 piecewise quartics on the same mesh.

Publié le :
DOI : 10.5802/smai-jcm.38
Classification : 65N30, 65N12, 76D07, 65N85

Guzmán, Johnny 1 ; Scott, L. Ridgway 2

1 Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
2 Departments of Computer Science and Mathematics, Committee on Computational and Applied Mathematics, University of Chicago, Chicago IL 60637, USA 
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     title = {Cubic {Lagrange} elements satisfying exact incompressibility},
     journal = {The SMAI Journal of computational mathematics},
     pages = {345--374},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
     volume = {4},
     year = {2018},
     doi = {10.5802/smai-jcm.38},
     mrnumber = {3883673},
     zbl = {1416.76109},
     language = {en},
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Guzmán, Johnny; Scott, L. Ridgway. Cubic Lagrange elements satisfying exact incompressibility. The SMAI Journal of computational mathematics, Tome 4 (2018), pp. 345-374. doi: 10.5802/smai-jcm.38

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