Year: 2011
International Journal of Numerical Analysis and Modeling, Vol. 8 (2011), Iss. 3 : pp. 391–409
Abstract
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 post-processed approximation converges with order $2k+1$ in the $L^2$-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 above-mentioned theoretical results are displayed.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2011-IJNAM-692
International Journal of Numerical Analysis and Modeling, Vol. 8 (2011), Iss. 3 : pp. 391–409
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Post-processing superconvergence discontinuous Galerkin methods Naghdi arches.