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 piecewise quartics on the same mesh.
DOI: 10.5802/smai-jcm.38
Johnny Guzmán 1; L. Ridgway Scott 2
@article{SMAI-JCM_2018__4__345_0, author = {Johnny Guzm\'an and L. Ridgway Scott}, 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}, zbl = {1416.76109}, mrnumber = {3883673}, language = {en}, url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.38/} }
TY - JOUR AU - Johnny Guzmán AU - L. Ridgway Scott TI - Cubic Lagrange elements satisfying exact incompressibility JO - The SMAI Journal of computational mathematics PY - 2018 SP - 345 EP - 374 VL - 4 PB - Société de Mathématiques Appliquées et Industrielles UR - https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.38/ DO - 10.5802/smai-jcm.38 LA - en ID - SMAI-JCM_2018__4__345_0 ER -
%0 Journal Article %A Johnny Guzmán %A L. Ridgway Scott %T Cubic Lagrange elements satisfying exact incompressibility %J The SMAI Journal of computational mathematics %D 2018 %P 345-374 %V 4 %I Société de Mathématiques Appliquées et Industrielles %U https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.38/ %R 10.5802/smai-jcm.38 %G en %F SMAI-JCM_2018__4__345_0
Johnny Guzmán; L. Ridgway Scott. Cubic Lagrange elements satisfying exact incompressibility. The SMAI Journal of computational mathematics, Volume 4 (2018), pp. 345-374. doi : 10.5802/smai-jcm.38. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.38/
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