Numerical Analysis and Applicable Mathematics
Title
A Robust HDG Method for Reissner-Mindlin Plate Problem
Authors
Gang Chen,a Xiaoping Xie*a and Yangwen Zhangb
aSchool of Mathematics, Sichuan University, Chengdu 610064, China
bDepartment of Mathematical Science, University of Delaware, Newark, DE 19716
*Corresponding author E-mail address: xpxie@scu.edu.cn (X. Xie)
Article History
Publication details: Received 05th May 2020; Revised 13th June 2020; Accepted 15th June 2020; Published 26th June 2020
Cite this article
Chen G.; Xie X.; Zhang Y. A Robust HDG Method for Reissner-Mindlin Plate Problems. Numer. Anal. Appl. Math., 2020, 1(1), 10-26.
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.
Keywords
Reissner-Mindlin plate; HDG method; error estimate; optimal convergence; uniformly stable
