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.
Bibliographical noteFunding Information:
1School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA. E-mail: firstname.lastname@example.org. 2School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA. E-mail: email@example.com. ★Supported in part by NSF Grant DMS-0411254 and by the University of Minnesota Supercomputing Institute.
- Discontinuous Galerkin method
- Timoshenko beams