A Modified Nonconforming 5-Node Quadrilateral Transition Finite Element (Advances in Applied Mathematics and Mechanics, 2021)
This paper analyzes a nonconforming 5-node quadrilateral transition finiteelement for Poisson equation. This element was originally proposed by Choiand 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 consistencyerror of this element is only $\mathcal{O}(h^{1/2})$ over the transition edges of the quadrilateralsubdivision. 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.