A Hybridizable Discontinuous Galerkin Method for Kirchhoff Plates

With the help of concepts of normal bending moment, twisting moment and effective transverse shear force, a hybridizable discontinuous Galerkin (HDG) method for Kirchhoff plates based on a second-order system is proposed in this paper, where piecewise polynomial of degree k-1 and  k are used to approximate moment and deflection respectively.In HDG method, Lagrange multipliers associated with deflection and its normal derivative are approximated by continuous kth order polynomial and piecewise (k-1)th order polynomial on the skeleton of triagulation, respectively.Optimal and superconvergent error estimates are proved under minimal regularity assumptions on the exact solution using some local lower bound estimates of a posteriori error analysis.Consequently the globally coupled degrees of freedom are only those associated with Lagrange multipliers which approximate deflection and its normal derivative at the edges of the triangulation.Furthermore, a new discrete deflection is constructed by postprocessing the solution of HDG method, which superconverges to deflection with order k+1 in broken H^1 norm.Finally, some numerical results are shown to demonstrate the theoretical results.