Locking-Free Optimal Discontinuous Galerkin Methods for a Naghdi-Type Arch Model

In this paper, we introduce and analyze discontinuous Galerkin methods for a Naghdi type arch model. We prove that, when the numerical traces are properly chosen, the methods display optimal convergence uniformly with respect to the thickness of the arch. These methods are thus free from membrane and shear locking. We also prove that, when polynomials of degree k are used, all the numerical traces superconverge with a rate of order h2k+1. Numerical experiments verifying the above-mentioned theoretical results are displayed.