TY - JOUR
T1 - Element-by-Element Post-Processing of Discontinuous Galerkin Methods for Naghdi Arches
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 391
EP - 409
PY - 2011
DA - 2011/08
SN - 8
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/692.html
KW - Post-processing, superconvergence, discontinuous Galerkin methods, Naghdi arches.
AB - <p style="text-align: justify;">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.</p>