@Article{IJNAM-10-2,
author = {},
title = {Local Error Estimates of the LDG Method for 1-D Singularly Perturbed Problems},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2013},
volume = {10},
number = {2},
pages = {350--373},
abstract = {<p style="text-align: justify;">In this paper local discontinuous Galerkin method (LDG) was analyzed for solving
1-D convection-diffusion equations with a boundary layer near the outflow boundary. Local error
estimates are established on quasi-uniform meshes with maximum mesh size $h$. On a subdomain
with $O(h\ln(1/h))$ distance away from the outflow boundary, the $L^2$ error of the approximations to
the solution and its derivative converges at the optimal rate $O(h^{k+1})$ when polynomials of degree
at most $k$ are used. Numerical experiments illustrate that the rate of convergence is uniformly
valid and sharp. The numerical comparison of the LDG method and the streamline-diffusion finite
element method are also presented.</p>},
issn = {2617-8710},
doi = {https://doi.org/2013-IJNAM-572},
url = {https://global-sci.com/article/83400/local-error-estimates-of-the-ldg-method-for-1-d-singularly-perturbed-problems}
}