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Volume 8, Issue 3
Element-by-Element Post-Processing of Discontinuous Galerkin Methods for Naghdi Arches

F. Celiker, L. Fan & Z. Zhang

Int. J. Numer. Anal. Mod., 8 (2011), pp. 391-409.

Published online: 2011-08

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  • 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.

  • Keywords

Post-processing, superconvergence, discontinuous Galerkin methods, Naghdi arches.

  • AMS Subject Headings

65M60, 65N30, 35L65

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-8-391, author = {F. Celiker, L. Fan and Z. Zhang}, title = {Element-by-Element Post-Processing of Discontinuous Galerkin Methods for Naghdi Arches}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2011}, volume = {8}, number = {3}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/692.html} }
TY - JOUR T1 - Element-by-Element Post-Processing of Discontinuous Galerkin Methods for Naghdi Arches AU - F. Celiker, L. Fan & Z. Zhang 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 -

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.

F. Celiker, L. Fan and Z. Zhang. (2011). Element-by-Element Post-Processing of Discontinuous Galerkin Methods for Naghdi Arches. International Journal of Numerical Analysis and Modeling. 8 (3). 391-409. doi:
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