Edge-Oriented Hexagonal Elements

Abstract

In this paper, two new nonconforming hexagonal elements are presented, which are based on the trilinear function space $Q_1^{(3)}$ and are edge-oriented, analogical to the case of the rotated $Q_1$ quadrilateral element. A priori error estimates are given to show that the new elements achieve first-order accuracy in the energy norm and second-order accuracy in the $L^2$ norm. This theoretical result is confirmed by the numerical tests.