(untitled) (Advances in Applied Mathematics and Mechanics, 2021)
We study the extensions of the Bogner-Fox-Schmit element to the whole family of Qk continuously differentiable finite elements on rectangular grids, for all k≥3, in 2D and 3D. We show that the newly defined C1 spaces are maximal in the sense that they contain all C1-Qk functions of piecewise polynomials. We give examples of other extensions of C1-Qk elements. The result is consistent with the Strang's conjecture (restricted to the quadrilateral grids in 2D and 3D). Some numerical results are provided on the family of C1 elements solving the biharmonic equation.