A new error analysis of Bergan's energy-orthogonal element for two-sided displacement obstacle problem of clamped plate

The main aim of this paper is to present a new error analysis of the Bergan's energy-orthogonal plate element for the two-sided displacement obstacle problem of clamped plate. Due to the exact solution does not belong to Hloc4(Ω), and the shape function and its first derivatives are discontinuous at the element's vertices, while all previous theoretical analysis always required the continuity of the shape function at element's vertices for the conventional finite elements, a series of novel approaches, including the definition of approximation subset, the constructions of a one-to-one transferring operator and an enriching operator, are developed to derive error estimates of order O(h) both in energy norm and L∞L∞-norm. It seems that these results have never been seen in the existing literature.