@Article{IJNAMB-5-188,
author = {MAHBOUB BACCOUCH},
title = { Superconvergence and <em>a Posteriori</em> Error Estimates of a Local Discontinuous Galerkin Method},
journal = {International Journal of Numerical Analysis Modeling Series B},
year = {2014},
volume = {5},
number = {3},
pages = {188--216},
abstract = {In this paper, we investigate the superconvergence properties and a posteriori error estimates of a local discontinuous Galerkin (LDG) method for solving the one-dimensional linear
fourth-order initial-boundary value problems arising in study of transverse vibrations of beams.
We present a local error analysis to show that the leading terms of the local spatial discretization
errors for the k-degree LDG solution and its spatial derivatives are proportional to (k+1)-degree
Radau polynomials. Thus, the k-degree LDG solution and its derivatives are O(h^{k+2}) superconvergent
at the roots of (k+1)-degree Radau polynomials. Computational results indicate that
global superconvergence holds for LDG solutions. We discuss how to apply our superconvergence
results to construct efficient and asymptotically exact a posteriori error estimates in regions where
solutions are smooth. Finally, we present several numerical examples to validate the superconvergence
results and the asymptotic exactness of our a posteriori error estimates under mesh
refinement. Our results are valid for arbitrary regular meshes and for P^k polynomials with k &#8805 1,
and for various types of boundary conditions.},
issn = {},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnamb/230.html}
}