TY - JOUR
T1 - On the Full C<sub>1</sub>-Q<sub>k</sub> Finite Element Spaces on Rectangles and Cuboids
AU - Zhang , Shangyou
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 701
EP - 721
PY - 2010
DA - 2010/02
SN - 2
DO - http://doi.org/10.4208/aamm.09-m0993
UR - https://global-sci.org/intro/article_detail/aamm/8356.html
KW - 
AB - <p style="text-align: justify;">We study the extensions of the Bogner-Fox-Schmit element to the whole
family of Q<sub>k</sub> continuously differentiable finite elements on rectangular grids, for
all k≥3, in 2D and 3D. We show that the newly defined C<sub>1</sub> spaces are maximal
in the sense that they contain all C<sub>1</sub>-Q<sub>k&nbsp;</sub>functions of piecewise polynomials. We
give examples of other extensions of C<sub>1</sub>-Q<sub>k</sub> elements. The result is consistent with
the Strang&#39;s conjecture (restricted to the quadrilateral grids in 2D and 3D). Some
numerical results are provided on the family of C<sub>1</sub> elements solving the biharmonic
equation.</p>