A Modified Nonconforming 5-Node Quadrilateral Transition Finite Element

Abstract

This paper analyzes a nonconforming 5-node quadrilateral transition finite element for Poisson equation. This element was originally proposed by Choi and Park [Computers and Structures, 32 (1989), pp. 295–304 and Thin-Walled Structures, 28 (1997), pp. 1–20] for the analysis of Mindlin plates. We show the consistency error of this element is only $\mathcal{O}(h^{1/2})$ over the transition edges of the quadrilateral subdivision. By modifying the shape functions with respect to mid-nodes, we get an improved version of the element for which the consistency error is $\mathcal{O}(h)$. Numerical examples are provided to verify the theoretical results.