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.
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Supported in part by NSF Grant DMS-0411254 and by the University of Minnesota Supercomputing Institute.
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Celiker, F., Cockburn, B. Element-by-Element Post-Processing of Discontinuous Galerkin Methods for Timoshenko Beams. J Sci Comput 27, 177–187 (2006). https://doi.org/10.1007/s10915-005-9057-5
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DOI: https://doi.org/10.1007/s10915-005-9057-5