Double set parameter finite element method for two-sided displacement obstacle problem of clamped plate

Double set parameter nonconforming finite element method (FEM) for the two-sided displacement obstacle problem of clamped plate is considered. Firstly, a double set parameter nonconforming triangular element (named Veubeke-Zienkiewicz element) is introduced, which has the same global dimension as Zienkiewicz element, and can pass the generalized patch test for any mesh. Secondly, we skillfully construct an enriching operator for connecting the Veubeke-Zienkiewicz and the C1-conforming Bell element spaces. With the help of this operator and an auxiliary obstacle problem built as a bridge between the continuous and discrete obstacle problems, we present the optimal order error estimates in the broken energy norm and L∞ norm, respectively. Finally, we establish a general framework of double set parameter nonconforming elements approximating for the two-sided displacement obstacle problem of clamped plate.