$$C^{0}$$-nonconforming tetrahedral and cuboid elements for the three-dimensional fourth order elliptic problem

In this paper, a theoretical framework is constructed on how to develop $$C^0$$-nonconforming elements for the fourth order elliptic problem. By using the bubble functions, a simple practical method is presented to construct one tetrahedral $$C^{0}$$-nonconforming element and two cuboid $$C^{0}$$-nonconforming elements for the fourth order elliptic problem in three spacial dimensions. It is also proved that one element is of first order convergence and other two are of second order convergence. From the best knowledge of us, this is the first success in constructing the second-order convergent nonconforming element for the fourth order elliptic problem.

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