A Robust HDG Method for Reissner-Mindlin Plate Problem

Abstract

We propose and analyze a hybridizable discontinuous Galerkin (HDG) method for Reissner-Mindlin plate problems. The method uses piecewise-polynomials of degree k(≥ 1) to approximate the transverse displacement and the displacement trace on inter-element boundaries, uses piecewise-polynomial vectors of degrees k and ‘, max(1; k - 1) ≤ ‘ ≤ k, to approximate respectively the rotation and the rotation trace on inter-element boundaries, and uses piecewise-polynomial vectors of degree k and piecewise-polynomial tensors of degree m, k - 1 ≤ m ≤ ‘, to approximate respectively the shear stress and the bending moment. We show that the HDG method is robust in the sense that the derived a priori error estimates are optimal and uniform with respect to the plane thickness t. Numerical experiments are performed to confirm our theoretical results.