New six-node and seven-node hexagonal finite elements

In this paper, we introduce a six-node and a seven-node hexagonal elements. Both elements are based on the rotated trilinear interpolation in terms of the three-directional coordinates. Optimal a priori error estimates are provided for the new elements by decomposing the consistency error into two parts that both can be estimated using the F-E-M test. Some numerical tests are carried out to verify the theoretical analysis. Comparisons to both the previously studied edge-oriented hexagonal elements and the traditional linear triangular elements are also provided to show the efficiency and superiority of the new six-node and seven-node hexagonal elements.