On the Full C1-Qk Finite Element Spaces on Rectangles and Cuboids (Advances in Applied Mathematics and Mechanics, 2021)
We study the extensions of the Bogner-Fox-Schmit element to the wholefamily of Qk continuously differentiable finite elements on rectangular grids, forall k≥3, in 2D and 3D. We show that the newly defined C1 spaces are maximalin the sense that they contain all C1-Qk functions of piecewise polynomials. Wegive examples of other extensions of C1-Qk elements. The result is consistent withthe Strang's conjecture (restricted to the quadrilateral grids in 2D and 3D). Somenumerical results are provided on the family of C1 elements solving the biharmonicequation.