TY - JOUR
T1 - Local Error Estimates of the LDG Method for 1-D Singularly Perturbed Problems
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 350
EP - 373
PY - 2013
DA - 2013/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/572.html
KW - Local discontinuous Galerkin method, singularly perturbed, local error estimates.
AB - <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>