Convergence analysis of a family of 14-node brick elements

In this paper, we will give convergence analysis for a family of 14-node elements which was proposed by Smith and Kidger (1992). The 14 DOFs are taken as the values at the eight vertices and the six face-centroids. For second-order elliptic problems, we will show that among all the Smith–Kidger 14-node elements, Type 1, Type 2 and Type 5 elements provide optimal-order convergent solutions while Type 6 element gives one-order lower convergent solutions. Motivated by our proof, we also find that the order of convergence of the Type 6 14-node nonconforming element improves to be optimal if we change the DOFs into the values at the eight vertices and the integration values on the six faces. We also show that Type 1, Type 2 and Type 5 keep the optimal-order convergence if the integral DOFs on the six faces are adopted.