Plate Elements With High Accuracy

High accuracy analysis of two nonconforming plate elements

“…In fact, the superconvergent estimates of the consistency error of some nonconforming elements for plate bending problems has been studied in references [20,24,25]. However, in view the result of Theorem 3.4, one cannot expect a superconvergent estimate of the consistency error of the incomplete biquadratic element.…”

The Quadratic Specht Triangle

“…To improve the accuracy of the element, we need to use higher order polynomial and improve the order of the consistency error simultaneously. The following result gives a sufficient condition for high order consistency error estimate [6]. We refer to [28] for related discussion.…”

“…The Specht triangle employs quadratic polynomial approximation and hence is a first order plate bending element, which likes many practical nonconforming plate bending elements such as Zienkwiecz triangle [4], Morley triangle [5], just name a few of them. There are some second order nonconforming plate bending elements scattered in the literature, such as the one proposed by one of the author in [6] from the notion of the double set parameter method and the one in [7], both elements have 12 degrees of freedom. Other quadratic plate bending elements, such as those in [8] and [9], have 16 degrees of freedom.…”

A quadrilateral nonconforming finite element for linear elasticity problem

“…As is known, the original DSP method is to construct effective plate elements for the fourth order problems. By using the DSP method, many simple nonconforming plate elements with more advantages over the conventional FEMs have been proposed (refer to [17,18,34,35]). In this work, we attempt to extend the DSP method to the low order nonconforming rotated Q 1 element.…”