Element-by-Element Post-Processing of Discontinuous Galerkin Methods for Timoshenko Beams

In this paper, we consider discontinuous Galerkin approximations to the solution of Timoshenko beam problems and show how to post-process them in an element-by-element fashion to obtain a far better approximation. Indeed, we show numerically that, if polynomials of degree p≥1 are used, the post-processed approximation converges with order 2p+1 in the L∞-norm throughout the domain. This has to be contrasted with the fact that before post-processing, the approximation converges with order p+1 only. Moreover, we show that this superconvergence property does not deteriorate as the the thickness of the beam becomes extremely small.