On the Full C1-Qk Finite Element Spaces on Rectangles and Cuboids

Abstract

We study the extensions of the Bogner-Fox-Schmit element to the whole family of Q_k 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-Q_k functions of piecewise polynomials. We give examples of other extensions of C₁-Q_k 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.