@Article{AAMM-2-6,
author = {Zhang, Shangyou},
title = {On the Full C<sub>1</sub>-Q<sub>k</sub> Finite Element Spaces on Rectangles and Cuboids},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2010},
volume = {2},
number = {6},
pages = {701--721},
abstract = {<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>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.09-m0993},
url = {https://global-sci.com/article/73664/on-the-full-csub1sub-qsubksub-finite-element-spaces-on-rectangles-and-cuboids}
}