Element-by-element Post-processing of Discontinuous Galerkin Methods for Naghdi Arches

In this paper, we consider discontinuous Galerkin approximations to the solution of Naghdi arches and show how to post-process them in an element-by-element fashion to obtain a far better approximation. Indeed, we prove that, if polynomials of degree k are used, the postprocessed approximation converges with order 2k+1 in the L2-norm throughout the domain. This has to be contrasted with the fact that before post-processing, the approximation converges with order k + 1 only. Moreover, we show that this superconvergence property does not deteriorate as the thickness of the arch becomes extremely small. Numerical experiments verifying the abovementioned theoretical results are displayed.