A new error analysis of Bergan's energy-orthogonal element for a plate contact problem

A nonconforming finite element method (FEM for short) is proposed and analyzed for a plate contact problem by employing the Bergan's energy-orthogonal plate element. Because the shape function and its first derivatives of this element are discontinuous at the element's vertices, which is quite different from the conventional finite elements used in the existing literature, some novel approaches, including interpolation operator splitting and energy orthogonality, are developed to present a new error analysis for deriving an optimal estimate of order O(h). At last, some numerical results are also provided to confirm the theoretical analysis.