Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 177-187 |
| Number of pages | 11 |
| Journal | Journal of Scientific Computing |
| Volume | 27 |
| Issue number | 1-3 |
| DOIs | |
| State | Published - Jun 2006 |
Bibliographical note
Funding Information:1School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA. E-mail: celiker@math.umn.edu. 2School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA. E-mail: cockburn@math.umn.edu. ★Supported in part by NSF Grant DMS-0411254 and by the University of Minnesota Supercomputing Institute.
Keywords
- Discontinuous Galerkin method
- Post-processing
- Superconvergence
- Timoshenko beams